Splice model and tile assembly for forming surfaces with less repetitive design and shape at triangular intersections of tile models

Abstract

The tile model and tile assembly form a surface with less repetitive design and shape at triangular intersections of the tile model. Each model, when located at a first directional angle, has the same perimeter composed of three outer curvilinear contours. The outer curved profile includes a concave side having a first region shape that is removed, the first region shape being added to an adjacent convex side that can seamlessly engage with concave sides of other tiles. Each tile model has three distinct interior top surface portions that project inwardly from three outer curvilinear profiles to three inner curvilinear profiles, which differs from the design of other tile models. The three different interior surface portions are configured to form a surface having a less repeating shape at a triangular intersection between three tile models, with one model at a first directional angle, a second model rotated 120 degrees, and a third model rotated 240 degrees.

Description

Copyright and Commercial Dye Statement

[0001] This patent document contains some copyrighted material. This patent document may show and / or describe matters that are or may be part of the trade dress of the rights holder. The copyright and trade dress owners have no objection to anyone copying the patent content disclosed in this patent document, which is disclosed in the form of a patent document or record of the Patent and Trademark Office, but retain all other copyright and trade dress rights. Information related to the application

[0002] This patent claims priority to provisional patent application 63 / 694,011, filed on September 12, 2024, entitled “Surface with a design and shape that is never repeated,” the entire contents of which are incorporated herein by reference. Background Technology Technical Field

[0003] The present invention relates to a limited number of tile models and tile assemblies of these tile models, which form surfaces with little repetition of design and shape at their triangular intersections.

[0004] Related technologies

[0005] To date, it has not been possible to lay ceramic tiles, marble, or other materials on walls or floors by combining a limited number of tile patterns at triangular intersections to create different shapes or designs (which rarely or never repeat). The global flooring and covering materials market is saturated with increasingly similar designs, sometimes tedious and easily replicated, which in some cases have had to appear in a regrettable but necessary form to achieve specific production costs and ensure marketability.

[0006] Continuously seeking practical solutions to create entirely new works with attractive and unique designs at a reasonable cost is an effective way for businesses to stand out in the market and, more importantly, to earn a living through professional conduct, not only in the market but also, first and foremost, among their employees and families.

[0007] After countless trials and experiments, new progress has been made in unique puzzle design. Now, with fewer than ten puzzle pieces or puzzle models disclosed in this invention, it is possible to manufacture less repetitive and aesthetically pleasing designs at a lower cost. Attached Figure Description

[0008] Figure 1A-1HFour types of block models are described in a limited number that can be used to form block components, creating surfaces with few repetitions of design and shape at the triangular intersections of the block models.

[0009] Figure 2A-2B A limited number of four tile models with arm-shaped spatter are described, which can be used to form tile components, forming surfaces with little repetition of design and shape at the triangular intersections of the tile models (e.g., the triangles may include or be the intersections of 1 / 3 irregular portions of the same intersection of the tile models).

[0010] Figures 3A-3B A limited number of four tile models are described, each having a periphery with an outer curved profile and an inner top surface portion, which can be used to form tile components, creating surfaces with minimal repetition of design and shape at the triangular intersections of the tile models.

[0011] Figures 4A-4C A finite number of three tile models are described, which can be used to form tile components, creating a geometric design with minimal repetition at the triangular intersection of the tile models.

[0012] Figures 5A-5D A limited number of six puzzle models are described, which can be used to form puzzle components, creating designs and shapes with few repetitions at the triangular intersections of the puzzle models.

[0013] Figures 6A-6B A limited number of six different tile models with varying thicknesses are described. These models can be used to form tile components or combinations, creating surfaces with minimal repetition of tile thickness designs and shapes at the triangular intersections of the tile models.

[0014] In this specification, elements appearing in the figures are assigned three-digit reference designators, where the most significant digit is the figure number and the two least significant digits are the element's specific identifier. Elements not described in conjunction with the figures are presumed to have the same characteristics and functions as previously described elements with the same least significant digit reference designators. Detailed instructions

[0015] This invention relates to a limited number of modular patterns and modular pieces of these patterns that can be used in modular assembly or installation, wherein the triangular intersections of these pieces can form surfaces with a shape design and / or shape that have minimal repetition. For example, compared to other modular pieces, simple standard industrial production using only 3, 4, 5, or 6 modular patterns described herein can achieve a minimally repetitive and aesthetically pleasing modular surface effect at a more reasonable cost, even when considering assembly or installation based on the modular patterns described herein.

[0016] In some cases, using a dozen or fewer (e.g., a limited number between 3 and 12) tile patterns to create a texture for a tile component with minimal repetition allows for the use and / or production of different proportions of each pattern or tile pattern used in the assembly, thereby optimizing production costs. Depending on the available raw material sizes on the market and the difficulty of cutting each individual pattern, some patterns or blanks may be cheaper to cut into tiles. This optimization reduces production costs because certain tile patterns (compared to other tile patterns used in the component) are cheaper to produce due to cheaper blanks, cheaper raw materials, and / or fewer expensive raw materials required for certain tiles. This optimization also reduces production costs because using more specific tile patterns (compared to other tile patterns used in the component) results in lower production costs due to the cheaper cutting of specific tile patterns and / or the lower cost of purchasing specific tile models available on the market.

[0017] This approach to use, selection, and / or optimization allows for a detailed study of the cost of the tile models used in the assembly (e.g., tiles within a tile model) to propose a version that uses a proportion of different numbers of tile models in the assembly at the lowest cost while maintaining the uniqueness of the assembly (e.g., minimal repetition and aesthetic appeal). This makes it possible to conduct a detailed study of the cost of different tile models used in the assembly and to select different numbers of different tile models used in the assembly to obtain the lowest or desired cost for all tiles while maintaining the uniqueness of the assembly. Each tile model may contain a greater or lesser percentage of tiles with the same mix, which each customer can choose according to their personal preferences. Tile manufacturers, retailers, assemblers, buyers, or flooring buyers can choose different numbers of tile mixes for each tile model to assemble to meet their respective preferences for cost and / or assembly uniqueness. This use, selection, and / or optimization may include excluding certain tile models from the use of the tiles.

[0018] The modular models (and the pieces within those models) described in this article can be used not only (e.g., assembled to) form surfaces for flooring or coverings, but also for forming furniture surfaces (e.g., their coverings), building facades, and other types of surfaces to which this concept can be applied. In some cases, the design of the modular models can be used for the “Blooming” series (e.g., see [link to related document]). Figure 1F Wood products with reduced size and thickness can be used for furniture exteriors and doors.

[0019] The description of a “tile,” “tile model,” or “model of tiles” can be or includes a tile shape, design, mosaic, pattern, shape, set, sample, instance, type, style, or name, such as those mentioned herein. The description of a “tile model” or “model of tiles” can be a single tile having selected or specific peripheral shapes, overall shapes, materials, designs, colors, sizes, etc., from which many tiles can be replicated; and / or manufactured based on the model. The description of a single tile or “tile” herein can be or includes a tile imitated according to a “tile model,” or a tile manufactured to be similar to the “tile model” in peripheral shapes, overall shapes, materials, designs, colors, sizes, etc. A single tile may be one of several tiles that are identical in appearance and function to a single tile model. Any of a finite number of tile models may be replicated by multiple tile models.

[0020] A "limited number" puzzle or puzzle pattern can be 3, 4, 5, or 6 pieces. It can be 3 to 12 pieces. A limited number of pieces can be 4 to 6 pieces. A limited number of pieces can be 3 to 7 pieces. A limited number of pieces can be 4 to 7 pieces.

[0021] Rarely repeating refers to the design and / or shape that is never repeated or nearly never repeated at the triangular intersection of the three pieces in the puzzle model.

[0022] Triangular intersections of the tile models or tiles may include or may include a 1 / 3 irregular section intersection area located at the intersection of three tile models (e.g., 1 / 3 or 1 / 3 pizza slice shaped surface of a tile edge). Triangular intersections of tiles may be or include the intersection of three distinct sections of three or more tile models forming a shape with few repetitions, and / or the intersection of three or more tile models with three distinct segmentation styles and / or colors forming a design with few repetitions, such as using a limited number of tile models as described herein.

[0023] Figure 1A-1H Four tile models Z, Y, X, and J (e.g., tiles of the tile model used) are described that can be used to form tile components or combinations, which form designs and shapes with few repetitions at the triangular intersections of the tile models, such as... Figure 1H As shown. Figure 1A The diagram shows top views of four different puzzle models T, each with a hexagonal shape, six corners (CH) and six sides (SH). All corners (CH) of puzzle model T form 120-degree interior angles, and all sides are of equal length. Lateral connections are maintained at three corners (A, B, and C); the SH sides of puzzle model T are modified by inverting the pieces twice on the two connecting sides. Starting with the hexagonal puzzle style, the six sides can fit together, offering greater versatility compared to the square style.

[0024] Figure 1B The diagram shows a top view of four tile models T1, each with six perimeter-side shapes A-, A+, B-, B+, C-, and C+, which cover the sides SH between the six corners CH. When each tile model is at the first direction angle OA, the six perimeter-side shapes are three pairs of connected or adjacent contour groups A-+, B-+, and C-+, which have three types of outer curvature shapes: A- and A+, B- and B+, and C- and C+. Figure 1BThree arrows are shown, representing three outer curved profiles: a concave (female) side (e.g., negative or inward) A-, B-, and C-, shaped by removing a first region from side SH to form the concave profile side; and an adjacent convex (male) side (e.g., positive or outward) side A+, B+, and C+, shaped by adding a corresponding profile of the first region to side SH to form the convex profile side. The actual material of the first region is neither removed (e.g., cut off) to form the concave profile side nor physically added (e.g., glued) to the adjacent convex profile side. Instead, the piece is cut according to the shape of the piece model without removing or adding any material to the actual piece. This also applies to other descriptions of the piece model, piece components, piece surfaces, and pieces of these models.

[0025] Figure 1C A top view of a finite number of four puzzle models Z, Y, X, and J is shown. Each model has a top surface (shown in the figure), a bottom surface (not shown), and a perimeter P formed by six perimeter sides A-, A+, B-, B+, C-, and C+ between six corners CH. When each puzzle model is at the first direction angle OA, these six perimeter sides form an approximately hexagonal shape, where three pairs of adjacent or connected sides A-+, B-+, and C-+ have three different outer curve profiles A- and A+, B- and B+, and C- and C+. As shown in the figure, the corresponding sides of the three pairs of adjacent sides are connected at corners A, B, and C or have puzzle side seams.

[0026] In some cases, the edges or perimeter shapes of each individual puzzle piece and its components can be treated in different or singular ways (e.g., variations) to create one or more patterns (e.g., edge or perimeter side profiles) that reference each other (e.g., at triangular intersections in the assembly structure with other puzzle pieces). In some cases, each pair (e.g., A, B, and C) of the six perimeter side profiles A-, A+, B-, B+, C-, and C+ can have variations of three different profiles ABC (as shown in the figure); two different shapes such as AAC, AAB, BBA, BBC, CCA, or CCB; and / or one shape AAA, BBB, or CCC. These variations can also be mixed. These variations can not only be used to better define each individual shape or simply define the shape of each puzzle piece, but also to create partial or overall decorative aesthetic effects using the edges themselves, according to personal preference.

[0027] Using the general hexagonal shapes or styles of the tile models Z, Y, X, and J offers the flexibility to combine the six sides, greatly enhancing the possibility of creating new designs that are more flexible than square shapes or styles; it also allows for the retention of references to the three alternative corners A, B, and C in the six corners CH; and / or the modification of the sides SH as needed by installing theminverted sides (e.g., removing the negative area and adding it to the positive area). Each of the tile models Z, Y, X, and J can serve as a tile model because they are not only individual tiles, but multiple of them can be used in a set of four tile models that can be assembled or installed to form tile assemblies such as ASSY.

[0028] Figure 1D Showing a top view of a limited number of four puzzle models Z, Y, X, and J assembled into a puzzle assembly ASSY, the puzzle assembly forms a surface S with a rarely repeated design and shape at the triangular intersection IX of the puzzle models (see...). Figure 1HThe distinctly irregular shapes of the six peripheral sides A-, A+, B-, B+, C-, and C+ form a roughly irregular hexagon that perfectly matches the other identical hexagons, allowing each tile model to rotate 120° relative to the previous tile model during installation, thus forming the assembly ASSY. Dividing the six sides SH into three pairs of sides, or portions A, B, and C, can be modified not only by curving and making them opposite (e.g., forming concave and convex shapes) of the hexagon's two consecutive sides, but also by laying out another tile model that connects to the same curved sides of the six peripheral sides, connecting at A- and A+, B- and B+, and C- and C+, as shown in the figure. In some cases, the convex sides of tiles A+, B+, and C+ perfectly match (or have a gap of up to 1, 2, or 3 mm) the corresponding concave sides A-, B-, and C- of another tile, as shown in the figure. An unexpected advantage of the tile model described in this article is that, compared to tiles with flat perimeters, tile models with curved perimeters provide better assembly joints during assembly or surface patching because the curved perimeters do not slide laterally or along each other as they do with flat tile sides. For example, the flat or straight sides of a hexagonal tile, or any other tile with flat sides (square, rectangle), may slide and shift during assembly. The tiles in the tile model described in this article do not slide because the curved perimeters of adjacent tiles match each other, and the interlocking curved shapes generate excessive friction, preventing lateral sliding.

[0029] The assembly ASSY has columns C1, C2, and C3 and rows R1, R2, and R3, which are random sequences of the tiles of tile models Z, Y, X, and J. Each tile model, except for edge tiles, is surrounded by six other tile models. Tiles can be fixed to their underlying surface, such as their bottom surface, by adhesive, pasting, nailing, screwing, epoxy resin, magnets, or other means. Tiles can be adjacent to each other, contacting, connecting, or fitting on their respective convex and concave sides, so that there are no gaps between the respective convex and concave sides. In some cases, each of the three outer curve profiles includes a concave side with a first region removed from the concave side, and an adjacent convex side with a first region proportional to the first region removed from the concave side and added to the convex side.

[0030] The assembly ASSY's sequence of tile models includes a first tile model, such as tile model J1, with an angle of OA. Each tile model connected to the first tile model is rotated 120 degrees (e.g., 1 / 3) clockwise relative to OA; or rotated 240 degrees (e.g., 2 / 3) clockwise relative to OA. For example, the tile models in row R1 are located at angle OA, the tile models in row R2 are rotated 240 degrees clockwise relative to the first OA angle, and the tile models in row R3 are rotated 120 degrees clockwise relative to the first OA angle.

[0031] A triangular intersection IX appears at the intersection of any three puzzle models. An intersection IX can be the intersection of any three puzzle models, including the three corners of the three different puzzle models. The puzzle models do not need to be different puzzle models, but they must have the same or corresponding corners among the three outer curved profiles A, B, or C that meet at the intersection. For example, intersection IX1 has the three corners C of puzzle models Y, Y, and Z. Each approximately hexagonal shape of the internal top surface of a puzzle model can be divided into three distinct parts, each defined by a pair of curved sides or each outer curved profile.

[0032] Figure 1E This is a top view showing a puzzle model or puzzle models Z, Y, X, and J with three different internal top surface parts. The puzzle models Z, Y, X, and J have three different internal top surface parts that project inwards from three outer curve profiles A- and A+, B- and B+, and C- and C+, extending to three pairs of adjacent internal sides. These internal sides form three internal curvature shapes connected at the LOC (Local Origin) of each puzzle model.

[0033] The puzzle model or puzzle Z has three distinct internal top surface portions AZ, BZ, and CZ, which protrude inward from three outer curved profiles A- and A+, B- and B+, and C- and C+, extending to connect to three pairs of adjacent internal side profiles CAZ and BAZ, CBZ and BAZ, and CAZ and CBZ, which have three inner curved profiles. As shown in the figure, the internal side profiles CAZ, CBZ, and BAZ connect at the internal location LOCZ.

[0034] The puzzle model, or puzzle Y, has three distinct internal top surface portions: AY, BY, and CY. These portions protrude inward from three outer curved profiles: A- and A+, B- and B+, and C- and C+, respectively, extending to connect to three pairs of adjacent internal side edges: CAY and BAY, CBY and BAY, and CAY and CBY, which have three inner curved profiles. As shown in the figure, the internal side edges CAY, CBY, and BAY connect at the internal location LOCY.

[0035] The puzzle model, or puzzle X, has three distinct internal top surface portions, AX, BX, and CX, which protrude inward from three outer curved profiles A- and A+, B- and B+, and C- and C+, extending to connect to three pairs of adjacent internal side profiles CAX and BAX, CBX and BAX, and CAX and CBX, which have three inner curved profiles. As shown in the figure, the internal side profiles CAX, CBX, and BAX are connected at the internal location LOCX.

[0036] The puzzle model or puzzle J has three distinct internal top surface portions, AJ, BJ, and CJ, which protrude inward from three outer curved profiles A- and A+, B- and B+, and C- and C+, respectively, extending to connect to three pairs of adjacent internal side edges CAJ and BAJ, CBJ and BAJ, and CAJ and CBJ, which have three inner curved profiles. As shown in the figure, the internal side edges CAJ, CBJ, and BAJ are connected at the internal position LOCJ.

[0037] Each puzzle piece has three distinct internal top surface portions A, B, and C that correspond to corners A, B, and C, with each surface portion having a near-quadrilateral or rhomboid shape with four curved sides. Each top surface portion may have internal angles of approximately 60°, 30°, 60°, and 30°. These three distinct internal top surface portions may be areas or sections of the top surface corresponding to or located at corners A, B, and C.

[0038] The contours (e.g., the top contour) of three distinct internal surface parts of one of the puzzle models Z, Y, X, and J differ from the contours of three distinct internal surface parts of any other puzzle model Z, Y, X, and J. The contour of each surface part A of a puzzle may differ from the contour of any other surface part A of puzzle models Z, Y, X, and J. In some cases, the contour of each internal surface part of puzzle models Z, Y, X, and J differs from the contours of all internal surface parts of puzzle models Z, Y, X, and J. The contour of each surface part A, B, or C of any puzzle may differ from the contours of all surface parts A, B, and C of all puzzle models Z, Y, X, and J.

[0039] At the intersection of three puzzle models in a finite number of puzzle models, three corresponding internal surface portions (e.g., AX, BX, or CX) are combined to form the top surface of a puzzle model with few repetitions in shape, such as at the triangular intersection of a finite number of puzzle models and the assembly of the puzzle models, ASSY. A puzzle model with a general hexagonal shape, whose sides are irregular or curved, has only two pairs of mutually compatible three external curve contours A- and A+, B- and B+, and C- and C+ (internal and external / positive and negative perimeter side contours). Therefore, the internal portions or top surface regions can be divided in different ways, dividing them into three contours or surface portions A, B, and C, as shown in Figure 4, which are different internally. Furthermore, referring to the three outer curve profiles A- and A+, B- and B+, and C- and C+, the three different inner top surface portions A, B, and C of each puzzle model (e.g., three specific single-piece shapes) can be arbitrarily divided into other styles or shapes; thereby creating more puzzle models (e.g., multiples of 3 for each top surface portion).

[0040] Figure 1F The diagram shows a top view of each puzzle model, or puzzle models Z, Y, X, and J with three different sectioned styles. As shown, each puzzle model, or Z, Y, X, and J, has three distinct internal surface sections, corresponding to corners A, B, and C with at least three different sectioned styles. In this case, each section is styled with three dividing lines dividing each internal surface section into four segments. However, other numbers of dividing lines and segments can also be considered.

[0041] The tile model or tile Z has three different partition patterns AZS, BZS, and CZS on the upper, surface, and / or interior (at, on, and / or in) of three different internal top surface portions AZ, BZ, and CZ. These three different partition patterns AZS, BZS, and CZS correspond to corners A, B, and C, and radiate from corners A, B, and C to each pair of adjacent internal side edges CAZ and BAZ, CBZ and BAZ, and CAZ and CBZ, respectively, as shown in the figure.

[0042] The puzzle model or puzzle Y has three different partition patterns AYS, BYS, and CYS on the upper layer, surface, and / or interior of three different internal top surface portions AY, BY, and CY. The three different partition patterns AYS, BYS, and CYS correspond to corners A, B, and C, and radiate from corners A, B, and C to each pair of adjacent internal side edges CAY and BAY, CBY and BAY, and CAY and CBY, respectively, as shown in the figure.

[0043] The puzzle model or puzzle X has three different partition patterns AXS, BXS, and CXS on the upper layer, surface, and / or interior of three different internal top surface portions AX, BX, and CX. These three different partition patterns AXS, BXS, and CXS correspond to corners A, B, and C, and radiate from corners A, B, and C to each pair of adjacent internal side edges CAX and BAX, CBX and BAX, and CAX and CBX, respectively, as shown in the figure.

[0044] The puzzle model or puzzle J has three different partition styles AJS, BJS, and CJS on the upper layer, surface, and / or interior of three different internal top surface portions AJ, BJ, and CJ, as shown in the figure. These three different partition styles AJS, BJS, and CJS correspond to corners A, B, and C, and radiate from corners A, B, and C to each pair of adjacent internal side edges CAJ and BAJ, CBJ and BAJ, and CAJ and CBJ, as shown in the figure.

[0045] These three different partition styles can be or include three distinct regions (e.g., three distinct inner top surface sections), each with a different style, fragment, partition, shape, line, texture, image (e.g., small images of stars, moons, birds, cats, rainbows, etc.) and / or texture. In some cases, the three distinct inner surface sections of a limited number of puzzle pieces are configured to form a flower pattern at each intersection.

[0046] Each tile model Z, Y, X, and J has three different partition styles (e.g., style, shape, line, texture, or grain) that differ from the three different partition styles of all other tile models Z, Y, X, and J. The partition style of each surface portion A of a tile may differ from the partition style of every other surface portion A of tile models Z, Y, X, and J. In some cases, the partition style of each inner surface portion of tile models Z, Y, X, and J may differ from the partition styles of all inner surface portions of all other tile models Z, Y, X, and J. The partition style of each surface portion A, B, or C of any tile may differ from the partition styles of all surface portions A, B, and C of all tile models Z, Y, X, and J.

[0047] At the intersection of three tile models in a finite number of tile models, three corresponding different partition styles (e.g., AXS, BXS, or CXS) are combined to form the top surface of the tile model with a minimal repetition of design, such as at the triangular intersection of a finite number of tile models and the assembly of the tile models, ASSY. The three different contours or internal surface portions defined on each irregular hexagonal tile with the same peripheral side profile (e.g., the same pair of curved edges or outer curve profile) can be better determined by using materials with different colors, surface treatments, and / or compositions, such as... Figure 1G As shown.

[0048] Figure 1G A top view is shown for each puzzle piece or puzzle model Z, Y, X, and J, each with three different colors. As shown, each puzzle model or puzzle model Z, Y, X, and J has three different internal surface parts A, B, and C, each with at least three different colors.

[0049] The puzzle model or puzzle Z has three different colors AZSC, BZSC, and CZSC on the upper, surface, and / or interior (at, on, and / or in) of three different internal top surface portions AZ, BZ, and CZ, respectively. The three different colors AZSC, BZSC, and CZSC correspond to corners A, B, and C, and radiate from corners A, B, and C to each pair of adjacent internal side edges CAZ and BAZ, CBZ and BAZ, and CAZ and CBZ, as shown in the figure.

[0050] The puzzle model or puzzle Y has three different colors AYSC, BYSC, and CYSC on the upper layer, surface, and / or interior of three different internal top surface portions AY, BY, and CY, respectively. The three different colors AYSC, BYSC, and CYSC correspond to corners A, B, and C, and radiate from corners A, B, and C to each pair of adjacent internal side edges CAY and BAY, CBY and BAY, and CAY and CBY, as shown in the figure.

[0051] The puzzle model or puzzle X has three different colors AXSC, BXSC, and CXSC on the upper layer, surface, and / or interior of three different internal top surface portions AX, BX, and CX, respectively. These three different colors AXSC, BXSC, and CXSC correspond to corners A, B, and C, and radiate from corners A, B, and C to each pair of adjacent internal side edges CAX and BAX, CBX and BAX, and CAX and CBX, as shown in the figure.

[0052] The puzzle model or puzzle Y has three different colors, AJSC, BJSC, and CJSC, on its upper layer, surface, and / or interior of three different internal top surface portions AJ, BJ, and CJ, respectively. These three different colors AJSC, BJSC, and CJSC correspond to corners A, B, and C, and radiate from corners A, B, and C to each pair of adjacent internal side edges CAJ and BAJ, CBJ and BAJ, and CAJ and CBJ, as shown in the figure.

[0053] The three different colors can be or include three distinct areas (e.g., three distinct interior top surface portions), each with a different color, finish, composition, gloss, hue, brightness, and tone. In some cases, the three different colors of a limited number of puzzle pieces are configured to form a flower pattern at each intersection.

[0054] These three different colors can be the same as (or only slightly different from) the three different colors of other puzzle models, so as to form a pattern with the same color design at each intersection. The three different colors of each puzzle model Z, Y, X, and J (e.g., color, finish, composition, gloss, hue, brightness, tone) can be the same as the three different colors of other puzzle models Z, Y, X, and J. The colors of each surface portion A, B, and C of the puzzle can be the same as the colors of each surface portion A, B, and C in other puzzle models Z, Y, X, and J. At the intersection of three puzzle models in a finite number of puzzle models, three corresponding colors (e.g., AXSC, BXSC, or CXSC) are combined to form the top surface of the puzzle model, which has a design with minimal repetition, for example, at the triangular intersection of a finite number of puzzle pieces or an assembly of puzzle models, ASSY.

[0055] A limited number (e.g., 4 tiles or tile models) can be randomly mixed, assembled, installed, or laid out, wherein the same pairs of curved sides A- and A+, B- and B+, and C- and C+ on the six peripheral sides must fit together to automatically create different shapes and / or designs at the intersection IX of each of the 3 tile models, such as... Figure 1H As shown.

[0056] Figure 1HA top view shows a limited number of four puzzle models Z, Y, X, and J assembled into a puzzle assembly ASSY. This assembly forms a surface S with a rarely repeating design and shape at the triangular intersection IX of the puzzle models. The distinctly irregular shapes of the six peripheral sides A-, A+, B-, B+, C-, and C+ form a generally irregular hexagon that perfectly matches the other identical hexagons, allowing each puzzle model to rotate 120° relative to the previous model during assembly to form the assembly ASSY. The assembly ASSY can be or includes puzzle models, or puzzle models that can be assembled or form a puzzle assembly or combination, to form a surface S with a rarely repeating (e.g., almost non-repeating) design and shape at the triangular intersection IX of these puzzle models.

[0057] Figure 1H The assembly ASSY can be a model that uses or includes a finite number of tiles, such as Z, Y, X, and J. Figure 1D The assembly is called ASSY. These tile models have six sides, which are divided into three pairs of sides or sections A, B, and C by bending and reversing them (e.g., convex or concave) so that they can be laid on top of each other with another tile model, and connected to each other with the same curved sides of the six peripheral sides so that they connect at A- and A+, B- and B+, and C- and C+, as shown in the figure. Although Figure 1D The assembly ASSY more clearly shows the pairing of the periphery of the top surface S of the puzzle model, but Figure 1H The assembly ASSY more clearly shows that the triangular intersection IX on the top surface S of the puzzle model has a shape and design with few repetitions.

[0058] The convex profile sides (the male-shaped side) of pieces A+, B+, and C+ can perfectly match (or have a gap of up to 1, 2, or 3 millimeters) the corresponding concave profile sides (the female-shaped side) of another piece, such as... Figure 1H As shown. The puzzle assembly ASSY has columns C1, C2, and C3 and rows R1, R2, and R3 formed by puzzle models Z, Y, X, and J in a random order sequence. Each puzzle model, except for the edge pieces, is surrounded by six other puzzle models. The pieces can be fixed to the surface beneath them, such as their bottom, by adhesive, glue, nailing, screwing, epoxy resin, magnets, or other means.

[0059] These sequences may include triangular intersections or connections between three puzzle models from a finite number of puzzle models, wherein the first puzzle model is located at a first orientation angle, the second puzzle model is rotated 120 degrees relative to the first orientation angle (e.g., 1 / 3 degree clockwise), and the third puzzle model is rotated 240 degrees relative to the first orientation angle (e.g., 2 / 3 of a turn clockwise). Each intersection may have the same or corresponding portions of three different internal surface parts of the first, second, and third puzzle models; and / or the intersection may have the same color as the first, second, and third puzzle models.

[0060] A random sequence of orders can be a finite number of random orders of each piece model in a finite number of puzzle models. In the example of a random sequence of orders for 4 puzzle models, the first sequence of 4 puzzles will have a random order of 4 pieces, then the second sequence of 4 puzzles (e.g., puzzles 5-8) will have another random order of 4 pieces, and so on, but with the restriction that each model in the 4 puzzle models appears in every sequence of 4 puzzles. In another example of a random sequence of orders for 4 puzzle models, every sequence of 8 puzzles will have a random order of 4 puzzle models, and so on, but with the restriction that each puzzle model must appear in one sequence of four puzzles. In yet another case, the 4 puzzle models may appear in a random order continuously, without being limited to each puzzle model appearing in one sequence of four puzzles. Random sequential sequences can be “truly random” (generated by physical phenomena such as radioactive decay), “pseudo-random” (generated by algorithms that appear random but are actually deterministic), or “quasi-random” (designed to distribute points uniformly in space, not truly random but suitable for certain specific applications) – the key difference between them lies in the degree to which they simulate true randomness and the methods used to generate them; “independent and identically distributed” (IID) sequences are also an important concept in probability theory for studying random sequences.

[0061] The puzzle pieces can be adjacent to each other, touching, connecting, or fitting together on their corresponding convex and concave sides, so that there are no gaps between the corresponding convex and concave sides, such as... Figure 1HAs shown. The corresponding surface portions of the three different internal surface portions of each of the three modular pieces in a finite number of modular pieces can be configured to form a shape with minimal repetition at the triangular intersection or the connection point of the three modular pieces. Of the three modular pieces, the first modular piece is, for example, modular piece Z1 with an orientation angle OA; the second modular piece Z2 is rotated 120 degrees (e.g., 1 / 3) relative to the first orientation angle OA; and the third modular piece Y1 is rotated 240 degrees (e.g., 2 / 3) relative to the first orientation angle OA. In some cases, the order of the modular pieces in the assembly ASSY includes: the first modular piece at the orientation angle OA, such as modular pieces Z1, Z2, or Y1, and each modular piece connected to the first modular piece, which is rotated 120 degrees (e.g., 1 / 3) clockwise relative to the orientation angle OA; or rotated 240 degrees (e.g., 2 / 3) clockwise relative to the orientation angle OA. For example, the tile model in row R1 is located at the orientation angle OA, the tile model in row R2 is rotated 240 degrees clockwise relative to the first orientation angle OA, and the tile model in row R3 is rotated 120 degrees clockwise relative to the first orientation angle OA.

[0062] The triangular intersection IX appears at the intersection of any three tile models. The intersection IX can be the meeting point of the three corners of three different tile models, a crossroads, and / or include a triangle. The tile models do not necessarily have to be different tile models, but they must have corners A, B, or C that meet at the intersection and have the same or corresponding three outer curve profiles. For example, the tile shape SHA2 with almost no repetition of outer curve profiles, the design DP2 of the inner surface portion, and the color design D2C of the intersection IX2 have the three corners C of the tile models Z, Y, and Y, as shown. Figure 1H As shown. Furthermore, the almost non-repeating tile shapes SHA3 of the outer curve profile, the design of the inner surface portion DP3, and the color design of the intersection point IX3 DC3 have the three corners B of the tile model Y, Y, and J, as... Figure 1H As shown.

[0063] The presence of pairs of adjacent, relatively curved sides (e.g., peripheral outer curve profiles) may necessitate laying each subsequent tile at a 120° rotation angle. This not only always alters the shape of the assembly and / or junctions but also the laying rotation angle of the tile model within the assembly. This produces surprising and almost never-before-seen visual effects at the assembly and / or junctions, such as... Figure 1HAs shown. Simply randomly installing multiple tile patterns results in tile shapes and / or designs that are almost never repeated, including at tile intersections. Using at least four patterns produces a probability or percentage at which the shapes people see are indeed rarely repeated, for example, appearing only zero, one, or two times in a 10-column, 10-row assembly, such as in 100 tiles. The limited number of four tile patterns provides an exciting aesthetic effect, making it look like a bespoke or personalized project. Now, this can be achieved with a simpler solution by producing a series of 3 to 7 standard tile patterns using the same patterns. This significantly reduces production and installation costs while maintaining the almost never-repeating shapes, designs, and aesthetics.

[0064] The descriptions in this article are merely examples; the same concepts can be used for other perimeter outer curvature shapes and / or internal top surface part shapes (e.g., geometric or abstract shapes). The descriptions in this article provide a model, assembly, and assembly process for a puzzle piece and its assembly using each regular hexagon, the negative / positive sides of the perimeter contour, and the resulting internal partitions or parts. This puzzle piece and its assembly are unique, e.g., with rarely repeating shapes and / or designs.

[0065] Figure 2A-2B Four finite number of puzzle models Z2, Y2, X2, and J2 are described, which can be used to form puzzle assemblies or combinations that create designs and shapes with minimal repetition at the triangular intersections of the puzzle models, such as... Figure 2B As shown. Figure 2A This is a top view showing each puzzle model, or each of the puzzle models Z2, Y2, X2, and J2 with three different partition styles. Each puzzle model, or Z2, Y2, X2, and J2, has three different internal surface sections, corresponding to corners A2, B2, and C2 with at least three different partition styles, as shown in the figure. In this case, each partition section is styled with 3, 4, or 5 dividing lines dividing each internal surface section into 4, 5, or 6 blocks. However, other numbers of dividing lines and segments can also be considered.

[0066] The puzzle model or puzzle Z2 has three different partition patterns AZS2, BZS2, and CZS2 on the upper layer, surface, and / or interior of three different internal top surface portions AZ2, BZ2, and CZ2, respectively. These three different partition patterns AZS2, BZS2, and CZS2 correspond to corners A2, B2, and C2, and radiate from corners A2, B2, and C2 to each pair of adjacent connected internal side edges CAZ2 and BAZ2, CBZ2 and BAZ2, and CAZ2 and CBZ2, as shown in the figure. The puzzle model or puzzle Z2 also includes three different arm-shaped splashes SAZ2, SBZ2, and SCZ2, which extend inward from the three corners A2, B2, and C2 to the interior position LOCZ2. These splashes are configured to form three-armed accents (AASA, AASB, and AASC) at some intersections of the first, second, and third tile models at IXA, IXB, and IXC, such as... Figure 2B As shown.

[0067] The mosaic model or mosaic Y2 has three different partition patterns AYS2, BYS2, and CYS2 on the upper layer, surface, and / or interior of three different internal top surface portions AY2, BY2, and CY2. These three different partition patterns AYS2, BYS2, and CYS2 correspond to corners A2, B2, and C2, respectively, and radiate from corners A2, B2, and C2 to each pair of adjacent connected internal side edges CAY2 and BAY2, CBY2 and BAY2, and CAY2 and CBY2, as shown in the figure. The mosaic model or mosaic Y2 also includes three different arm-shaped splashes SAY2, SBY2, and SCY2, which extend inward from the three corners A2, B2, and C2 to the interior position LOCY2. These splashes are configured to form three-arm decorative areas AASA, AASB, and AASC at some intersections IXA, IXB, and IXC of the first, second, and third mosaic models, as shown in the figure. Figure 2B As shown.

[0068] The puzzle model or puzzle X2 has three different partition patterns AXS2, BXS2, and CXS2 on the upper layer, surface, and / or interior of three different internal top surface portions AX2, BX2, and CX2, respectively. These three different partition patterns AXS2, BXS2, and CXS2 correspond to corners A2, B2, and C2, and radiate from corners A2, B2, and C2 to each pair of adjacent connected internal side edges CAX2 and BAX2, CBX2 and BAX2, and CAX2 and CBX2, as shown in the figure. The puzzle model or puzzle X2 also includes three different arm-shaped splashes SAX2, SBX2, and SCX2, which extend inward from the three corners A2, B2, and C2 to the interior position LOCX2. These splashes are configured to form three-arm decorative areas AASA, AASB, and AASC at some intersections IXA, IXB, and IXC of the first, second, and third puzzle models, as shown in the figure. Figure 2B As shown.

[0069] The mosaic model or mosaic J2 has three different partition patterns AJS2, BJS2, and CJS2 on the upper layer, surface, and / or interior of three different internal top surface portions AJ2, BJ2, and CJ2, respectively. These three different partition patterns AJS2, BJS2, and CJS2 correspond to corners A2, B2, and C2, and radiate from corners A2, B2, and C2 to each pair of adjacent connected internal side edges CAJ2 and BAJ2, CBJ2 and BAJ2, and CAJ2 and CBJ2, as shown in the figure. The mosaic model or mosaic J2 also includes three different arm-shaped splash spots SAJ2, SBJ2, and SCJ2, which extend inward from the three corners A2, B2, and C2 to the internal position LOCJ2. These splash spots are configured to form three-arm decorative areas AASA, AASB, and AASC at some intersections IXA, IXB, and IXC of the first, second, and third mosaic models, as shown in the figure. Figure 2B As shown. The intersection of the first, second, and third puzzle pieces, IX2, lacks an arm, as... Figure 2B As shown.

[0070] Figure 2A The three different partition styles can be or include three different regions (e.g., three different inner top surface sections), each region having a different style, segment, partition, shape, line, texture and / or feel. Figure 2A The style in may be different from Figure 1F The styles are different. Figure 2A The three outer curve profiles, the inner surface portion, the three inner curve profiles, and the internal position of each puzzle piece model may be related to... Figure 1BThe differences in -H. The three different partition styles (e.g., style, shape, lines, texture, and / or feel) for each tile model Z2, Y2, X2, and J2 may differ from the three different partition styles of any other tile model Z2, Y2, X2, and J2, such as... Figure 1F The shown separation pattern. The three different arm-shaped splatter spots can be or include three different regions (e.g., three different inner top surface portions), each region having a different splatter spot shape, leaf shape, vein shape, flame shape, torch shape, and / or finger shape. The three different arm-shaped splatter spots may or may not be located between the three outer curve profiles of each piece model.

[0071] At the intersection of three puzzle models in a finite number of puzzle models, corresponding portions of three different arm-shaped splashes (such as those located at corners A2, B2, and C2) are combined together to form the top surface of the puzzle model, which has a design with few repetitions, such as at the triangular intersection of the puzzle assembly ASSY2 in a finite number of puzzle models.

[0072] The three different arm-shaped splatter patterns may have three different widths and three different lengths. The three different arm-shaped splatter patterns may taper towards the center of the tile or location LOCZ2, COZY2, LOCX2, LOCJ2, and terminate before reaching that location. In some cases, the three different arm-shaped splatter patterns have different patterns; for example, corner A has a narrower width and a longer length; corner B has a wider width and a shorter length; and corner C has a medium width and a medium length. In some cases, these patterns can be interchanged as long as the same splatter pattern is located at the corresponding corners A, B, or C. In other cases, they do not need to be located at the corresponding corners. Each corresponding different arm-shaped splatter pattern SA, SB, and SC of the three different arm-shaped splatter patterns can have the same splatter pattern and color (e.g., see...). Figure 1G Texture, shadow and / or gloss, such as forming a design at the intersection of arm-shaped splatter spots or patterned splatter spots.

[0073] Each of the three different arm-shaped spatters (e.g., spatter, color, surface finish, composition, polish, shading, brightness, hue) of each tile model Z2, Y2, X2, and J2 can be identical to each of the three different arm-shaped spatters of the other tile models Z2, Y2, X2, and J2. The arm-shaped spatters of each corner A2, B2, and C2 of the tile can be identical to the arm-shaped spatters of the other corners A2, B2, and C2 of the tile models Z2, Y2, X2, and J2. In some cases, Figure 2A In a finite number of tile models, three distinct internal surface sections are configured to form a blooming flower pattern at each intersection of the components, for example... Figure 2BThe assembly ASSY2 in the component; the three-arm decorative area is configured to form a central stamen pattern of a flower in some of the flower blooming patterns of the component.

[0074] In some cases, the tile models Z2, Y2, X2, and J2 also include, for example: Figure 1G The color shown. In this case, with Figure 1G In contrast, splatter spots may have or be a fourth color.

[0075] A limited number, such as 4 puzzle pieces or Figure 2A The modular model can be randomly mixed, assembled, installed, or laid out, with the same 3-joined pairs on the 6 peripheral sides having 3 different external curve profiles at corners A2, B2, and C2 (see, for example, see...). Figure 1B-1C And the six peripheral sides of 1H (A- and A+; B- and B+; and C- and C+), these connection pairs must fit together to automatically create different shapes and / or designs at each intersection IX of the three tile models, such as... Figure 2B As shown.

[0076] Figure 2B A top view shows a limited number of four puzzle models Z2, Y2, X2, and J2 assembled into a puzzle assembly ASSY2. This assembly forms a surface S2 with a minimally repetitive design and shape at the triangular intersection IX of the puzzle models. On the six peripheral sides (e.g., see...),... Figure 1B At angles A2, B2, and C2 of the sides A-, A+, B-, B+, C-, and C+ in -C and 1H, three outer curve profiles exhibit distinctly irregular shapes, forming a roughly or irregular hexagon that perfectly matches other identical hexagons. During assembly, each puzzle model can be rotated 120° compared to the previous model to form assembly ASSY2. Assembly ASSY2 can be or includes puzzle pieces, or puzzle models that can be assembled into or form puzzle assemblies or combinations, to form surfaces S2 with minimal repetition (e.g., almost no repetition) of design and shape at the triangular intersections IX2 of these puzzle models.

[0077] Figure 2B The assembly ASSY2 in the middle can be with Figure 1H Similar to the assemblies in ASSY, these use or include a limited number of tile models, such as Z2, Y2, X2, and J2, instead of tile models Z, Y, X, and J. These tile models have six sides, divided into three pairs of sides or sections A, B, and C by bending and reversing them (e.g., convex or concave) to connect another tile model to the same bent sides of the six peripheral sides, thus connecting at A- and A+, B- and B+, and C- and C+ as shown in the figure. Although Figure 1HThe assembly ASSY in the middle more clearly shows the color design of the intersection IX, but Figure 2B The assembly ASSY2 in the model more clearly shows the triangular intersection IX of the top surface S of the puzzle model Z2, Y2, X2 and J2 with few repeated shapes and designs, such as arm shapes and flower stamens.

[0078] Figure 2B The gaps, rows, columns, random order, adjacency, intersection, and / or rotations between the tile models Z2, Y2, X2, and J2 of the mid-assembly ASSY2 can be compared with... Figure 1D and / or Figure 1H The modular model Z, Y, X, and J of the mid-assembly ASSY are identical.

[0079] Assembly ASSY2 is or comprises a finite number of modular models Z2, Y2, X2, and J2, which have three different arm-shaped spatters (e.g., SAZ2, SBZ2, and SCZ2). These spatters extend inward from three corners A2, B2, and C2 between three outer curve profiles (e.g., AZ2, BZ2, and CZ2), forming three-arm decorative areas AASA, AASB, and AASC at the intersections IXA, IXB, and IXC of the first, second, and third modular models, as shown below. Figure 2B As shown.

[0080] The puzzle models Z2, Y2, X2, and J2 and / or ASSY2 show that each flower, with three different inner surface portions of the three puzzle models at each intersection, transforms into a blooming flower with a rarely repeating shape (rotated relative to direction OA); and, at each intersection, the central stamen (of each flower) of the three different arm-shaped splashes of the three puzzle models changes to a stamen with a rarely repeating design (optionally, rotated relative to direction OA). These rarely repeating shapes and designs make the puzzle models and assemblies unique and constantly evolving, ultimately achieving an aesthetic effect that can only be obtained through highly precise and luxurious custom puzzle assembly design.

[0081] The description herein also applies to embodiments with only one or two peripheral outer curve profiles and internal top surface portion shapes, which can employ the same principles as described above. These one or two profiles and portions provide modular models, components, and assembly processes that utilize one or two profiles and parts on the concave / convex sides of each regular hexagon, peripheral profiles, and the resulting internal partitions or portions, which are unique and form unique components, for example, having shapes and / or designs with few repetitions.

[0082] Figures 3A-3BA limited number of four puzzle models, Z3, Y3, X3, and J3, are described. Each has only one peripheral outer curve profile and one internal top surface shape, which can be used to form puzzle assemblies or combinations. These models create designs and shapes with minimal repetition at the triangular intersections of the puzzle models, such as... Figure 3B As shown. Figure 3A This is a top view showing each puzzle model, or puzzle models Z3, Y3, X3, and J3 with one different partitioning style. Each puzzle model, or puzzle models Z3, Y3, X3, and J3, has one distinct internal surface portion corresponding to corner A3, but no portions corresponding to corners B3 and C3; and only one corresponding distinct partitioning style, as shown in the figure. In this case, the style of each partitioned area is that each internal surface portion is divided into four blocks by three dividing lines. However, other numbers of dividing lines and blocks can also be considered.

[0083] The puzzle model or puzzle Z3 has a different partition pattern AZS3 on the upper layer, surface and / or interior (at, on, and / or in) of a different internal top surface portion AZ3. This different partition pattern AZS3 may correspond to corner A3 and radiate from corner A3 to each pair of connected adjacent internal sides CAZ3 and BAZ3, as shown in the figure.

[0084] The puzzle model or puzzle Y3 has a different partition pattern AYS3 on the upper layer, surface and / or interior of a different internal top surface portion AY3. This different partition pattern AYS3 may correspond to corner A3 and radiate from corner A3 to each pair of connected adjacent internal sides CAY3 and BAY3, as shown in the figure.

[0085] The puzzle model or puzzle X3 has a different partition pattern AXS3 on the upper layer, surface and / or interior of a different internal top surface portion AX3. This different partition pattern AXS3 may correspond to corner A3 and radiate from corner A3 to each pair of connected adjacent internal sides CAX3 and BAX3, as shown in the figure.

[0086] The puzzle model or puzzle J3 has a different partition style AJS3 on the upper layer, surface and / or interior of a different internal top surface portion AJ3. This different partition style AJS3 may correspond to corner A3 and radiate from corner A3 to each pair of connected adjacent internal side edges CAJ3 and BAJ3, as shown in the figure.

[0087] When each piece model is located at the first direction angle OA, each of the separation styles AZS3, AYS3, AXS3 and AJS3 has an outer curve profile A- and A+.

[0088] Figure 3AIt also demonstrates that each internal top surface portion AZS3, AYS3, AXS3, and AJS3 has three different colors on its upper layer, surface, and / or interior. As shown in the figure, these three different colors radiate from corner A3 to each pair of adjacent connected internal sides CA and BA. These three different colors can be randomly arranged. In some cases, these colors are as follows: Figure 1G The colors shown. In some cases, each internal top surface portion of AZS3, AYS3, AXS3, and AJS3 has the following colors. Figure 2A-2B The splash pattern shown.

[0089] It has a different internal top surface portion and / or partition style, each protruding inward from one outer curve profile A- and A+ of corner A3 to a pair of interconnected internal side edges (e.g., CAZ3 and BAZ3) to form an internal curve profile, which are interconnected at internal positions LOCZ3, LOCY3, LOCX3 and LOCJ3 respectively.

[0090] Each pair of adjacent internal sides of tile models Z3, Y3, X3, and J3 is different from the internal sides of all other tile models Z3, Y3, X3, and J3. In some cases, the partitioning style of each tile model Z3, Y3, X3, and J3 is different from the partitioning style of all other tile models Z, Y, X, and J.

[0091] At the intersection of three types of puzzle models in a finite number of puzzle models, the parts with different internal top surface sections and / or partition styles and / or colors are combined to form the top surface S3 of a puzzle model with a few repetitive designs, such as at the triangular intersection of the puzzle assembly ASSY3 in a finite number of puzzle models.

[0092] A finite number, for example Figure 3A The finite number of four puzzle pieces or puzzle models shown can be randomly mixed, assembled, installed, or laid out, wherein there are three outer curve profiles at corners A2, B2, and C2 (see, for example, see...). Figure 1B-1C The same three pairs of connected tiles (A- and A+; B- and B+; and C- and C+) on the six peripheral sides of 1H must match each other to spontaneously form different shapes and / or designs at each intersection of the three tile models IX, such as... Figure 3B As shown.

[0093] Figure 3B A top view shows a limited number of four puzzle models Z3, Y3, X3 and J3 assembled into a puzzle assembly ASSY3, which forms a surface S3 with a few repetitive designs and shapes at the triangular intersection IX3 of these puzzle models. Figure 3BThe hexagonal tile T0 is shown to be randomly mixed and laid out with a limited number of four tile models Z3, Y3, X3, and J3, but not mixed at the intersection IX3. In some cases, the pattern of each dividing zone includes 3 or 4 dividing lines to form 4 or 5 blocks in each inner surface section; the 3 different inner surface sections of the limited number of tile models are configured to form a blooming flower pattern at each intersection.

[0094] In some cases, the three different colors of each puzzle model are the same as the three different colors of one different inner surface portion of another finite number of puzzle models. In some cases, the three different colors of each puzzle model in the finite number of puzzle models are configured to form a design with little repetition at the triangular intersection IX3. In some cases, the three different colors of each puzzle model are randomly selected. In some cases, the three different colors of the finite number of puzzle models are configured to form a flower pattern at each intersection. For example, the almost non-repeating puzzle shape SHA4 is used for the outer curve outline, design DP4 is used for the inner surface portion, and design DC4 is used for the color of the intersection IX31, where puzzle models J3, J3, and Z3 have three corners A, such as... Figure 3B As shown.

[0095] 6 peripheral sides (for example, see Figure 2A The distinctly irregular shapes of the three outer curved profiles at corner A3 (sides A-, A+) form a general or irregular hexagon that perfectly matches other identical hexagons, allowing each puzzle model to be rotated 120° relative to the previous model during assembly to form assembly ASSY3. Assembly ASSY3 may be or include puzzle models, or puzzle models that can be assembled into or form a puzzle assembly or combination, to form surfaces S3 with minimal repetition (e.g., almost no repetition) of design and shape at the triangular intersections IX3 of these puzzle models.

[0096] Figure 3B The assembly ASSY3 and Figure 1H The assembly ASSY is similar, but uses or includes a limited number of tile models T0, Z3, Y3, X3, and J3 instead of tile models Z, Y, X, and J. Figure 3B The gaps, rows, columns, random order, adjacency, intersection, and / or rotation of the tile models T0, Z3, Y3, X3, and J3 in the mid-assembly ASSY3 may be related to... Figure 1H The mid-assembly assembly ASSY has the same pieces.

[0097] The puzzle models Z3, Y3, X3, and J3 and / or ASSY3 demonstrate that each flower, formed by one different internal surface portion of the three puzzle models at each intersection, transforms into a blooming flower with a rarely repeating shape (rotated relative to direction OA) and a rarely repeating design. These rarely repeating shapes and designs make the puzzle models and assemblies unique and constantly evolving, ultimately achieving the aesthetic effect that only highly precise and luxurious custom puzzle assembly designs can provide. Therefore, this solution allows for the creation of personalized designs at a reasonable cost.

[0098] As stated above, the above concepts also apply to models with fewer than four tiles or to embodiments of tile models. Furthermore, the above concepts can be applied to geometries such as angled linear segments.

[0099] Figures 4A-4B A finite number of three puzzle models, Z4, Y4, and X4, are described, which can be used to form puzzle components or combinations, creating rarely repeating shapes and geometric patterns at the triangular intersections of the puzzle models, such as... Figure 4C As shown, the three modular models Z4, Y4 and X4 are all configured to form an assembly ASSY4 with a surface S4 having a shape and geometry with little repetition at the intersections, by using angled shapes of linear segments. Figure 4A The diagram shows top views of three finite number of tile models: Z4, Y4, and X4. Each tile model has six perimeter-side shapes: A4-, A4+, B4-, B4+, C4-, and C4+, which overlap the sides SH between the six corners. When each tile model is at the first orientation angle OA, the six perimeter-side shapes are three pairs of connected or adjacent side pairs: A4-+, B4-+, and C4-+. These side pairs have line segments of three outer angled shapes: A4- and A4+, B4- and B4+, and C4- and C4+. Angled shapes can consist of 2 to 6 linear segments, forming an angle at each intersection. Figure 4A In the -C example, there are 4 linear segments, and each intersection between them forms 3 different angles.

[0100] Figure 4AThree arrows are shown, wherein the three external bevel shapes include a concave (e.g., negative or inward) shape with sides A4-, B4-, and C4-, whose first region is removed from side SH to form a concave side, and adjacent convex (e.g., positive or outward) shapes with sides A4+, B4+, and C4+, whose corresponding first regions are added to side SH to form a convex side.

[0101] Figure 4B A top view of a limited number of three puzzle models Z4, Y4, and X4 is shown. Each puzzle has a top surface (shown in the figure), a bottom surface (not shown), and a perimeter P formed by six peripheral sides A4-, A4+, B4-, B4+, C4-, and C4+. When each puzzle model is at a first orientation angle OA, the six peripheral sides form a hexagon with approximately six sides. The three pairs of connected or adjacent sides A4-+, B4-+, and C4-+ have three external oblique angle shapes A4- and A4+, B4- and B4+, and C4- and C4+ with linear segments. As shown in the figure, the corresponding two sides of the three pairs of adjacent sides connect or achieve lateral joining of the puzzle at angles A4, B4, and C4. The puzzle models Z4, Y4 and X4 can all be used as puzzle models because they are not only individual puzzles, but multiple puzzles can also be used in a set of three puzzle models, and then used for assembly or installation to form a puzzle assembly such as ASSY4.

[0102] The convex sides of puzzle models Z4, Y4, and X4 seamlessly connect with the corresponding concave sides of another puzzle model Z4, Y4, and X4. Each of the puzzle models Z4, Y4, and X4 has three distinct corresponding internal top surface portions (e.g., AZ4, BZ4, and CZ4) that protrude inward from three external beveled shapes A4- and A4+, B4- and B4+, and C4- and C4+, extending to three single or connected internal sides. These internal sides have three internal angled linear segments that connect at internal locations LOCZ4, LOCY4, and LOCX4 within each puzzle model. The three distinct internal surface components (e.g., AZ4, BZ4, and CZ4) of each puzzle model in the finite number of puzzle models Z4, Y4, and X4 are different from the other three distinct internal surface components of the finite number of puzzle models Z4, Y4, and X4. The corresponding surface portions of three different internal surface parts of each of the three puzzle models Z4, Y4, and X4 are configured to form a surface S4 at the triangular intersection IX4 between the three puzzle models Z4, Y4, and X4. This surface has a shape with few repetitions, wherein the first puzzle model is located at a first orientation angle OA, the second puzzle model is rotated 120 degrees relative to the first orientation angle OA, and the third puzzle model is rotated 240 degrees relative to the first orientation angle OA. A finite number, such as three puzzle models, can be randomly mixed, assembled, installed, or laid out, wherein the same connection pairs among the six peripheral angled sides A4- and A4+, B4- and B4+, and C4- and C4+, must be able to fit together to spontaneously form different shapes and / or designs at each intersection IX4 of the three puzzle models, such as... Figure 4C As shown.

[0103] Figure 4C A top view shows a limited number of three puzzle models Z4, Y4, and X4 assembled into a puzzle assembly ASSY4. This assembly forms surface S4 at the triangular intersection IX4 of the puzzle models, a surface with a rarely repeating design and shape. The distinctly irregular shapes of the six peripheral sides A4-, A4+, B4-, B4+, C4-, and C4+ form a roughly or irregular hexagon that perfectly matches the other identical hexagons, allowing each of the three puzzle models to be rotated 120° relative to the previous one during assembly to form assembly ASSY4. Assembly ASSY4 can be or includes puzzle models, or puzzle models that can be assembled into or form a puzzle assembly or combination, to form surface S4 at the triangular intersection IX4 of these puzzle models with a rarely repeating (e.g., almost non-repeating) design and shape.

[0104] Figure 4C The assembly ASSY4 and Figure 1H The assembly ASSY is similar, but uses or includes a limited number of tile models Z4, Y4, and X4 instead of tile models Z, Y, X, and J. Figure 4C The gaps, rows, columns, random order, adjacency, intersection, and / or rotation of the Z4, Y4, and X4 tiles in the mid-assembly ASSY4 can be compared with... Figure 1H The modular model of the mid-assembly ASSY is the same.

[0105] In some cases, the three different colors of each puzzle model Z4, Y4, and X4 are the same as the three different colors of the other puzzle models of Z4, Y4, and X4. In other cases, the three different colors of each puzzle model of a finite number of puzzle models Z4, Y4, and X4 are configured to form a design with minimal repetition at the triangular intersection IX4. Each of the three puzzle models Z4, Y4, and X4 is configured to form an assembly ASSY4 having a surface S4 with minimal repetition of angled shapes at the intersection IX4, formed at each intersection IX4 of the three puzzle models Z4, Y4, and X4 by joined pairs of angled sides A4- and A4+, B4- and B4+, and C4- and C4+ using linear segments. Each of the three tile models Z4, Y4, and X4 is configured to form an assembly ASSY4, whose surface S4 has a few repeating geometric patterns, achieved by using three different and corresponding inner top surface portions (e.g., AZ4, AY4, and AX4) at each intersection IX4 of the three tile models Z4, Y4, and X4. Each of the three tile models Z4, Y4, and X4 is configured to form an assembly ASSY4, whose surface S4 has a few repeating geometric patterns, achieved by using three different and corresponding colors for the inner top surface portions (e.g., AZ4, AY4, and AX4) at each intersection IX4 of the three tile models Z4, Y4, and X4. Each of a finite number of tile models Z4, Y4, and X4 can be configured to form an assembly ASSY4, whose surface S4 has a few repeating geometric patterns, achieved by using three different and corresponding colors for the inner top surface portions at the intersections. Each geometric pattern can be a square, triangle, rectangle, quadrilateral, or other shape with linear sided shapes, such as the square geometric pattern GS1 at the intersection IX4SQ1, the square geometric pattern GS2 at the intersection IX4SQ2, the quadrilateral geometric pattern GS3 at the intersection IX4SQ3, and the quadrilateral geometric pattern GS3 at the intersection. The triangular geometric pattern GS3 at IX4SQ3.

[0106] As described above, the concept also applies to embodiments with four or more tile models or tile models. For example, Figure 1A-1H The tile models Z, Y, X, and J in the model can be obtained through... Figure 1A-1H It is expanded by adding the tile model K and W.

[0107] Figures 5A-5D A limited number of six puzzle models Z, Y, X, J, K, and W are described for forming puzzle components or combinations, which can form designs and shapes with few repetitions at the triangular intersections of the puzzle models, such as... Figure 5D As shown. For example, it can be done by... Figure 1A-1H Add tile models K and W to attach tile models Z, Y, X, and J.

[0108] Figure 5A A top view of a limited number of six tile models Z, Y, X, J, K, and W is shown. Each tile model has a top surface (shown in the figure), a bottom surface (not shown), and a perimeter P formed by six peripheral sides A-, A+, B-, B+, C-, and C+ between the six corners CH. When each tile model is at the first direction angle OA, as shown... Figure 1A-1D As shown in the puzzle models Z, Y, X, and J, the six peripheral sides form a hexagon with approximately six sides. Three pairs of connected or adjacent sides, A-+, B-+, and C-+, have three different external curve profiles: A- and A+, B- and B+, and C- and C+. As shown, the corresponding sides of the three adjacent pairs of sides connect or achieve lateral joining of the puzzle pieces at corners A, B, and C. Puzzle models Z, Y, X, J, K, and W can all be used as puzzle models because they are not only individual puzzle models, but multiple pieces can be used in a set of six puzzle models, and thus can be used, assembled, or installed to form puzzle assemblies such as ASSY5. Figure 5A Six puzzle models Z, Y, X, J, K, and W are shown, each with three distinct inner top surface portions. These portions protrude inward from three outer curve profiles, such as shapes A- and A+, B- and B+, and C- and C+, extending to connect to three pairs of adjacent inner sides. These inner sides have the three inner curve profiles that connect at the LOC (Location of Origin) within each puzzle model. Figure 1A-1D The model of the middle piece is shown in Z, Y, X and J.

[0109] Figure 5BThis is a top view showing a puzzle model or puzzle pieces Z, Y, X, J, K, and W with three different partition styles. The puzzle model or puzzle pieces Z, Y, X, J, K, and W have three different internal surface portions corresponding to corners A, B, and C. Corners A, B, and C have at least three different partition styles, such as... Figure 1A-1D The tile model Z, Y, X, and J are shown in the diagram. In this case, each dividing region is styled as having 3 dividing lines dividing each internal surface portion into 4 blocks. However, other numbers of dividing lines and blocks can also be considered.

[0110] Figure 5C This is a top view showing each puzzle model or puzzle piece Z, Y, X, J, K, and W with three different colors on their respective inner top surface portions. Each puzzle model or puzzle piece Z, Y, X, J, K, and W has three different colors corresponding to corners A, B, and C, such as... Figure 1A-1D The three different colors of the Z, Y, X and J tiles in the model are shown.

[0111] A limited number (e.g., 6 tiles or tile models) can be randomly mixed, assembled, installed, or laid out, wherein the same pairs of curved sides A- and A+, B- and B+, and C- and C+ on the 6 peripheral sides must fit together to automatically create different shapes and / or designs at each intersection IX5 of the 3 tile models, such as... Figure 5D As shown.

[0112] Figure 5D A top view is shown showing a limited number of six puzzle models Z, Y, X, J, K, and W assembled into a puzzle assembly ASSY5. This assembly forms surface S5 at the triangular intersection IX5 of the puzzle models. This surface has a design and shape with few repetitions, for example, as... Figure 1A-1D As shown, ASSY forms surface S at the triangular intersection IX of the mosaic model Z, Y, X and J, which has a design and shape with few repetitions.

[0113] Instead of all finite number of tile models having a uniform thickness, producers can choose to produce tile models with three different thicknesses, thereby achieving continuous variations in shape and thickness and obtaining a more striking aesthetic effect than simple planar tile models. Therefore, the above concept also applies to embodiments of finite number of tile models with different tile thicknesses THA, THB, and THC (e.g., between the top and bottom surfaces) in three different internal surface sections (e.g., AZ, BZ, and CZ).

[0114] Figures 6A-6BA limited number of six tile models of varying thicknesses—Z, Y, X, J, K, and W—are described. These models can be used to form tile components or combinations, creating unique tile thickness designs and shapes at the triangular intersections of the tile models, such as... Figure 6B As shown. For example, it can be done by... Figure 1A-1H Add tile models K and W to attach tile models Z, Y, X, and J. Figure 6A The concept of thickness Z in the tile model can be extended to any one or more internal surface portions (e.g., AZ, BZ, and CZ) of the finite number of tile models in this paper. For example, different thicknesses THA, THB, and THC can be applied to each of the A, B, and C portions (respectively) of 3, 4, 5, 6, or 7 tile models. A different thickness THA, THB, and THC can be applied only to the A, B, or C portions of 3, 4, 5, 6, or 7 tile models. The bottom surface of each tile can be flat, and the thicknesses THA, THB, and THC cause the height of the three portions (A, B, and C) of each tile to vary. The top surface of each portion can be curved at or near the boundaries between the three portions to avoid edges between the portions. In other cases, the top surface of each portion is flat, and edges exist between the portions based on the different thicknesses. In some cases, the thickness THA is less than the thickness THB, and the thickness THB is less than the thickness THC.

[0115] Figure 6A A top-view perspective of six tile models Z, Y, X, J, K, and W is shown. When each tile model is at a first orientation angle OA, each tile model has a top surface (shown in the figure), a bottom surface (not shown), and three pairs of connected or adjacent side pairs A-+, B-+, and C-+. These side pairs have three different external curve profiles: A- and A+, B- and B+, and C- and C+. Tile model Z has thicknesses THA, THB, and THC in three distinct internal surface portions AZ, BZ, and CZ (e.g., between the top and bottom surfaces). This concept can be extended to any number of internal surface portions. This concept can be extended to any number of tile models from a finite number of tile models. At each intersection (e.g., IX, IXA, IX3, IX4, IX5, etc.), the thicknesses THA, THB, and THC are identical in all three tile models.

[0116] The three distinct internal surface components AZ, BZ, and CZ of the tile model Z have different thicknesses THA, THB, and THC, respectively. In this case, thickness THA is less than thickness THB, and thickness THB is less than thickness THC. However, the thickness differences between the AZ, BZ, and CZ components may vary. This concept applies to any or all AZ, BZ, and CZ components, and to any or all finite number of tile models. Each intersection of the three tile models has the same thickness because the thicknesses of these three distinct internal surface components are the same in the first, second, and third tile models. A finite number of tile models, such as six tile models, or tile models with thicknesses THA, THB, and THC, can be randomly mixed, assembled, installed, or laid out, wherein the same pairs of curved sides A- and A+, B- and B+, and C- and C+ on the six peripheral sides must fit together to automatically create different shapes and / or designs at each intersection of the three tile models IX6A, IX6B, and IX6C, such as... Figure 6B As shown.

[0117] Figure 6B A top view shows a limited number of six puzzle models Z, Y, X, J, K, and W assembled into a puzzle assembly ASSY6. This assembly forms surfaces S6 with minimal repetition in design and shape at the triangular intersections IX6A, IX6B, and IX6C of the puzzle models. Figure 1A-1D The ASSY shown here forms a surface S with a design and shape that is rarely repeated at the triangular intersection IX of the mosaic model Z, Y, X, and J. Each intersection IX6A, IX6B, and IX6C has a different thickness THA, THB, and THC, respectively.

[0118] In some cases, each thickness THA, THB, and THC exists across the entire surface of each of the three distinct internal surface portions AZ, BZ, and CZ. That is, positions LOCZ, LOCY, LOCX, and LOCJ may have thicknesses THA, THB, and THC. In other cases, the thicknesses THA, THB, and THC gradually decrease in thickness from the six peripheral sides to the position LOC of each tile model, becoming the thickness of the position LOC (e.g., it could be any one of thicknesses THA, THB, or THC). That is, positions LOCZ, LOCY, LOCX, and LOCJ may have the same thickness, which is one of THA, THB, or THC.

[0119] At the intersection of three tile models (e.g., tiles of a certain type) in a finite number of tile models, three corresponding thicknesses THA, THB, and THC are combined to construct the top surface of the tile model, which has a rarely repeating design, such as at the triangular intersection of the tile assembly ASSY6 in a finite number of tile models. In this case, the rarely repeating design is formed by different intersections with different thicknesses THA, THB, and THC, or by adding to the surface through these different intersections. In each tile model in a finite number of tile models, the corresponding thicknesses of the same three thicknesses can be configured to form a surface with a rarely repeating design at the triangular intersection. In some cases, the intersection of three tiles with different thicknesses has the same thickness. In some cases, the center of each tile model has the same thickness, for example, different thicknesses are located at the periphery of the tile and shrink to a single thickness at the center of the tile.

[0120] This invention includes a puzzle assembly comprising a finite number of 4 to 6 puzzle models (and the assembly of their puzzles). Each puzzle model has a top surface, a bottom surface, and a hexagon located at a peripheral corner. The hexagon's perimeter has three pairs of consecutive outer sides (2 consecutive outer sides), wherein the first pair of consecutive outer sides has a first curve, and the second pair of consecutive outer sides has a second curve opposite to the first curve, thus requiring another puzzle piece to be mounted onto the first or second curve to have the second or first curve. Each top surface of the assembly is internally divided into three distinct sections extending from the three pairs of consecutive outer sides to the center of the puzzle piece; the three distinct sections of each puzzle piece differ from the three distinct sections of other puzzle pieces. The assembly randomly mixes the finite number of puzzle models on the surface such that the first and second curves of the three pairs of consecutive outer sides of one puzzle piece correspond to the opposite second and first curves of the three pairs of consecutive outer sides of another puzzle piece, respectively. The combination features a random mix of six tile peripheries (e.g., edges, borders, or borders) surrounding the central tile model of each tile model. Each of the six tile peripheries is rotated 1 / 3 or 120 degrees clockwise or counterclockwise relative to the orientation of each central tile model to create a visual effect that is almost never repeated. Each of the three distinct internal surface portions of each tile model in the finite number of tile models is unique to each or all of the three distinct internal surface portions of the other three tile models in the finite number of tile models. The corresponding surface portions of the three distinct internal surface portions of each tile model in the finite number of tile models are configured to form surfaces with rarely repeated shapes at the triangular intersections between the three tile models in the finite number of tile models, wherein the first tile model has a first orientation angle, the second tile model is rotated 120 degrees relative to the first orientation angle, and the third tile model is rotated 240 degrees relative to the first orientation angle.

[0121] The novel tiles, tile models, and tile components described herein allow for the creation of surfaces whose shapes and designs almost always appear different, using only a limited number of industrially produced tiles or tile models. By modifying the peripheral outer curved profile, the shape, style, color, and / or thickness of the inner top surface portion, the same concept can be personalized according to individual preferences and styles (geometric, modern, floral, organic, abstract, or other) while maintaining the same, self-evident installation system or method. The concepts in this paper include embodiments that develop the potential of hexagonal-style tile models that allow the six sides of the peripheral outer curved profile to fit together and divide it into three inner top surface portions: not only by bending the consecutive two sides of the hexagon and making them opposite, thus forcing it to be installed with another tile having the same curved sides, but also by dividing the same hexagon internally into three distinct sections, each defined by a pair of curved sides of the same shape. Using these embodiments, a limited number of tiles or tile models can be created that, once assembled or laid on a surface and randomly mixed with identical curved sides that must match each other, spontaneously form different shapes. These embodiments include pairs of adjacent sides, curved opposite faces, which may result in each subsequent tile installation being limited to a 120° rotation, not only always changing the shape but also the angle of rotation during installation: this produces surprising and almost never-repeating visual effects. The industrial production of these limited numbers of tiles or tile models now makes it possible to achieve shapes at the intersection of tile components and assemblies through simple and rapid installation, shapes and designs that rarely look alike and are almost never repeated.

[0122] Each puzzle piece or puzzle model may include or be made of at least one of the following materials: wood, plywood, solid wood, wood shavings / particleboard, paper, plastic, linoleum, composite material, ceramic tile, marble, or ceramic. Each puzzle piece, puzzle model, and / or puzzle component may be attached to (e.g., mounted, assembled on, or covered over) a surface of a wall, ceiling, table, balcony, fireplace (exterior or interior), and / or floor. Each puzzle piece, puzzle model, or component may include an adhesive (e.g., glue, nails, screws, epoxy, resin, magnet) to hold the piece to the surface. Each puzzle piece, puzzle model, or component may be or may be configured to be assembled on surfaces indoors, outdoors, in varying weather conditions, underwater, on bridges, on building exteriors, and / or in spaces.

[0123] The tile model in this article can be a tile model of surface tiles, used to form tile components to create surfaces with rarely repeating designs and shapes at the triangular intersections of the tile model. The tile model can be used to form tile surfaces composed of multiple unique tile types (e.g., tile models) with unique connecting surfaces. The tile model can also be used to form surfaces with rarely repeating patterns composed of multiple unique tile types and connecting surfaces.

[0124] Conclusion

[0125] In this specification, the embodiments and examples shown should be considered as examples and not as limitations on the disclosed or claimed apparatus and methods. Although many examples involved in this specification contain combinations of specific method steps or system elements, it should be understood that these steps and elements can be combined in other ways to achieve the same objective. Regarding flowcharts, steps can be added or removed, and the steps shown can be combined or further refined to implement the methods described herein. Steps, elements, and features discussed only in one embodiment do not necessarily have a similar effect in other embodiments.

[0126] As used herein, “multiple” or “quantity” refers to two or more. As used herein, a “group” of things may include one or more such things. As used herein, whether in the specification or the claims, terms such as “comprising,” “including,” “carrying,” “having,” “containing,” and “involving” should be understood as open-ended, meaning “including but not limited to.” Only the transitional phrases “consisting of” and “consisting essentially of” are closed or semi-closed transitional phrases in the claims. The use of ordinal numbers such as “first,” “second,” and “third” to modify a claim feature element does not imply any priority, order, or priority of one claim element relative to another, nor does it imply the chronological order of the steps in the method; they are merely labels used to distinguish two claim elements with the same name (but using ordinal numbers). In this specification, “and / or” means that the listed items are alternatives, but alternatives also include any combination of the listed items.

Claims

1. A tile model for forming tile components, used to create surfaces with minimal repetition of design and shape at the triangular intersections of the tile model, the tile model comprising: A limited number of 4 to 6 puzzle models, each puzzle model having a top surface, a bottom surface and a perimeter with 6 sides, wherein, when each puzzle model is at a first orientation angle, the 3 pairs of connected side pairs of the 6 sides have 3 kinds of external curve profiles. Each of the three external curve profiles includes a concave side having the shape of a first region removed from the concave side, and an adjacent convex side having the shape of a first region added to the convex side. In this model, the convex side of one puzzle piece is seamlessly connected to the corresponding concave side of another puzzle piece; Each puzzle model has three distinct and corresponding internal top surface portions, which protrude inward from three outer curve profiles to three pairs of connected internal sides, which have three inner curve profiles connected at an internal position in each puzzle model; In this finite number of puzzle models, each of the three different internal surface parts of each puzzle model is different from the three different internal surface parts of the other puzzle models in the finite number of puzzle models, and In this finite number of puzzle models, the corresponding surface portions of the three different internal surface portions of each puzzle model are configured to form a surface with few repetitions in shape at the triangular intersection between the three puzzle models of the finite number of puzzle models. The first puzzle model is located at a first orientation angle, the second puzzle model is rotated 120 degrees relative to the first orientation angle, and the third puzzle model is rotated 240 degrees relative to the first orientation angle.

2. The puzzle model as claimed in claim 1, wherein each triangular intersection is an intersection of the three corners of three different puzzle models in a finite number of puzzle models, the intersection having a corresponding outer curve profile, or an intersection of 1 / 3 irregular portions of the edges of the puzzles of three different puzzle models.

3. The puzzle model as described in claim 1 further includes a puzzle component having a finite number of columns and rows of a random sequence of puzzle models, the columns and rows being interconnected on corresponding convex and concave sides such that no gaps are formed between the corresponding convex and concave sides; in, The sequence includes a first puzzle model placed at a first orientation angle, and each puzzle model rotated by one of 120 degrees or 240 degrees relative to the first orientation angle and connected to the first puzzle model.

4. The puzzle model as described in claim 3, wherein, The random sequence is the random order of each piece model in the finite number of piece models.

5. The modular model as described in claim 1, wherein the three different internal surface portions have at least three different separation patterns; wherein, The three different partitioning styles of each tile model in the finite number of tile models are different from the three different partitioning styles of the other tile models in the finite number of tile models; In this context, the three different partition styles of each of the finite number of puzzle models are configured to form a surface with few repetitive designs at the triangular intersections.

6. The puzzle model as described in claim 1, wherein the three different internal surface portions of each finite number of puzzle models have three different colors; and the three colors of each puzzle model in the finite number of puzzle models are the same three colors; in, The three identical colors of each of the three tiles in the finite number of tile models are configured to form a surface with little repetition at the triangular intersection.

7. The puzzle model as described in claim 1, wherein, The sequence includes the triangular intersection between three of the finite number of puzzle models, wherein the first puzzle model is located at the first orientation angle, the second puzzle model is rotated 120 degrees relative to the first orientation angle, and the third puzzle model is rotated 240 degrees relative to the first orientation angle.

8. The tile model as claimed in claim 1, wherein each intersection has corresponding portions of three different internal surface portions of the first, second, and third tile models; and wherein, The intersection has the same color as the first, second, and third puzzle pieces.

9. The puzzle model as claimed in claim 1, wherein each puzzle model comprises one of wood, plywood, solid wood, particleboard, paper, plastic, linoleum, composite material, ceramic tile, marble, or ceramic; and further comprises a puzzle surface formed by a plurality of puzzle pieces of the puzzle model, wherein, The assembly is attached to one of the surfaces of a wall, ceiling, table, or floor; and the assembly includes an adhesive for attaching the puzzle model to the surface.

10. The puzzle model as described in claim 1, wherein, The limited number of tile models also include arm-shaped splashes of a fourth color extending inward from the three corners between the three outer curve contours to form three-arm decorative areas at some intersections of the first, second, and third tile models.

11. The puzzle model as described in claim 10, wherein, The three different internal surface portions of the finite number of puzzle pieces are configured to form a flower pattern at each intersection; and the three-armed decorative area is configured to form a stamen pattern in the center of the flower in a portion of the flower pattern.

12. The modular model of claim 1, wherein the three different internal surface portions each have a different thickness; and wherein, The intersection has the same thickness in three different internal surface portions of the first, second, and third piece models; and In this finite number of tile models, the corresponding thicknesses of the same three thicknesses of each tile model are configured to form a surface with little repetition at the triangular intersection.

13. A mosaic model for forming mosaic components to create surfaces with minimal repetition of design and shape at the triangular intersections of the mosaic model, said mosaic model comprising: A limited number of 4 to 6 puzzle models, each puzzle model having a top surface, a bottom surface and a perimeter with 6 sides, wherein when each puzzle model is at a first orientation angle, the 4 said sides are hexagonal sides and a pair of connected side pairs have an outer curve profile. The outer curve profile includes a concave side having a shape of a first region removed from the concave side, and an adjacent convex side having a shape of a first region added to the convex side. In this model, the convex side of one puzzle piece is seamlessly connected to the corresponding concave side of another puzzle piece; Each puzzle model has a distinct internal top surface portion that protrudes inward from an outer curved profile to a pair of connected internal sides, each internal side having an inner curved profile that is connected at position LOC within each puzzle model. In this finite number of tile models, one distinct internal surface portion of each tile model is different from one distinct internal surface portion of each of the other tile models in the finite number of tile models, and In this finite number of puzzle models, one different internal surface portion of each puzzle model is configured to form a surface with little repetition of shape at the triangular intersection between the three puzzle models of the finite number of puzzle models, wherein the first puzzle model is located at a first orientation angle, the second puzzle model is rotated 120 degrees relative to the first orientation angle, and the third puzzle model is rotated 240 degrees relative to the first orientation angle.

14. The puzzle model of claim 13, wherein each triangular intersection is the intersection of three corners of three different puzzle models comprising the finite number of puzzle models.

15. The modular model as described in claim 13, wherein a different internal surface portion has at least one different partitioning pattern; wherein, Each of the different partitioning styles of the finite number of tile models is different from one of the different partitioning styles of the other tile models in the finite number of tile models. In this configuration, one different partitioning style for each of the finite number of tile models is configured to form a surface with minimal repetition at the triangular intersections.

16. The puzzle model as described in claim 13, wherein one different internal surface portion of each finite number of puzzle models has three different colors; and the three different colors of each puzzle model in the finite number of puzzle models are the same three colors; in, The three different colors of each of the limited number of puzzle models are configured to form a surface with a minimal repetition of designs at the triangular intersections.

17. The puzzle model as described in claim 16, wherein, The three different colors of each tile in the finite number of tile models are randomly selected, and In this model, three different colors in the limited number of blocks are configured to form a flower pattern at each intersection.

18. A mosaic model for forming mosaic components to create surfaces with minimal repetition of design and shape at the triangular intersections of the mosaic model, the mosaic model comprising: A limited number of 4 to 6 puzzle models, each puzzle model has a top surface, a bottom surface and a perimeter with 6 sides, and when each puzzle model is in a first orientation angle, 3 pairs of connected side pairs have 3 external bevel shapes. Each of the three external beveled shapes includes a concave side having a shape of a first region removed from the concave side, and an adjacent convex side having a shape of a first region added to the convex side. In this model, the convex side of one puzzle piece is seamlessly connected to the corresponding concave side of another puzzle piece; Each puzzle model has three distinct, corresponding internal top surface portions that protrude inward from three external beveled shapes to three pairs of connected internal sides, which have three internal beveled shapes that connect at an internal location within each puzzle model. In this finite number of puzzle models, each of the three distinct internal surface portions of each puzzle model is different from the three distinct internal surface portions of the other puzzle models in the finite number of puzzle models. In this finite number of puzzle models, the corresponding surface portions of the three different internal surface portions of each puzzle model are configured to form a surface with few repetitions in shape at the triangular intersection between the three puzzle models. The first puzzle model is located at a first orientation angle, the second puzzle model is rotated 120 degrees relative to the first orientation angle, and the third puzzle model is rotated 240 degrees relative to the first orientation angle.

19. The puzzle model as described in claim 18, wherein, The angled shape can consist of 2 to 6 linear segments, which form an angle at each intersection; and Each triangular intersection is an intersection of the three corners of three different puzzle models, which include a finite number of puzzle models.

20. The puzzle model as described in claim 18, wherein, The finite number of puzzle pieces are configured to form an assembly whose surface has a slightly repetitive bevel shape at the junction by utilizing the paired beveled sides of connected linear segments.

21. The puzzle model as described in claim 18, wherein, Each of the finite number of puzzle pieces is configured to form an assembly whose surface forms a geometric pattern with few repetitions by utilizing three different and corresponding internal top surface portions at the intersection.

22. The puzzle model as described in claim 18, wherein, Each of the finite number of puzzle pieces has three distinct internal surface portions with three different colors; the three distinct colors of each puzzle piece in the finite number of puzzle pieces are the same three colors. In this design, the three different colors of each of the finite number of puzzle models are configured to form a surface with a geometric pattern that has few repetitions at each triangular intersection.

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