Double Geometric Hinge Connected Magnetic Puzzle

Abstract

The present invention provides a dual geometry puzzle. A dual geometry puzzle includes a continuous loop of polyhedrons connected to one another via hinges. The polyhedrons include a first type of polyhedron having a first geometric shape and a second type of polyhedron having a different second geometric shape. Each of the polyhedrons includes at least one magnet disposed proximate to at least one face thereof. The puzzle is configurable between a first inverted configuration and a second inverted configuration. The first and second inverted configurations are congruent parallelepipeds, e.g., having holes therethrough. All outermost surfaces of the first inverted configuration and all outermost surfaces of the second inverted configuration are mutually exclusive.

Description

Detailed Description of the Invention

[0001] (Related Applications) This application claims priority to and the benefit of U.S. Provisional Patent Application No. 63 / 298,718, filed January 12, 2022, the entire contents of which are incorporated herein by reference. [Technical Field]

[0002] The present invention relates to the toy and puzzle field. [Background technology]

[0003] Puzzles have appealed to generations as games, toys, educational aids, therapeutic devices, and the like. Such puzzles can be configured in different geometric configurations, as shown, for example, in Asano's UK Patent Application No. GB ​​2,107,200 and Schaedel's U.S. Patent No. 6,264,199 B1. As taught in the prior art, the attributes of any particular polyhedral puzzle depend heavily on the geometry and hinge connection configuration of that particular puzzle. For example, the folding puzzle taught in Schaedel consists of 24 identical isosceles tetrahedron bodies formed by four triangular faces with angles of approximately 70.53°, 54.74°, and 54.74°. The tetrahedrons are joined to each other at their base (longest) edges and can be manipulated into a rhombic dodecahedron in "many different ways." However, Schaedel does not teach anything else that can be done in many different ways to achieve the geometry of a rhombic dodecahedron. In reality, as one skilled in the art will appreciate, such puzzles have an infinite number of different combinations of variables, including the number of polyhedral faces and edges, the interior angles and edge lengths of the polyhedrons, the number of polyhedrons, whether all of the polyhedrons are the same, how the polyhedrons are arranged, the locations of the hinges between the polyhedrons, and other variables. Moreover, because of these seemingly infinite combinations of variables and the unpredictable results of changing the variables relative to one another, even a small change in one variable can alter the attributes of the entire puzzle, usually in ways that are detrimental to the functionality and appeal of the puzzle itself.

[0004] Therefore, new puzzles with different geometries and exciting new attributes are needed. Summary of the Invention

[0005] The present invention provides a puzzle having multiple solid polyhedron bodies hinged to form a continuous loop. By performing different movement sequences, the puzzle can be manipulated into many different configurations that are visually and tactilely interesting. For example, the polyhedrons can be configured to be manipulated about the loop axis of the continuous loop (i.e., flipping the puzzle from inside out) and / or switched about hinges (e.g., bridge strips) connecting adjacent polyhedrons. The specific geometry of the polyhedrons and the specific hinge connection relationships defined by the hinges allow the puzzle to be manipulated into many different geometric configurations and to be inverted in two different ways (flipping from inside out). Additionally, multiple magnets with complementary polarities are configured into the entire puzzle. Advantageously, the magnets stabilize the puzzle in many configurations.

[0006] In one aspect, the present invention provides a dual geometry puzzle comprising a continuous loop of polyhedra hinged together by a hinge connection device (e.g., a hinge), wherein a first of the plurality of polyhedra are first kind of polyhedra having a first geometric shape and a second of the plurality of polyhedra are second kind of polyhedra having a different second geometric shape, each of the polyhedra including at least one magnet disposed proximate at least one face thereof.

[0007] In another aspect, the present invention provides a dual geometry puzzle. The dual geometry puzzle includes a continuous loop of polyhedra connected to one another via hinges, wherein a first of the plurality of polyhedra are polyhedra of a first kind having a first geometric shape and a second of the plurality of polyhedra are polyhedra of a second kind having a different second geometric shape, each of the polyhedra including at least one magnet disposed adjacent to at least one face thereof. The continuous loop of polyhedra is configurable between a first inverted configuration and a second inverted configuration, the first and second inverted configurations being congruent parallelepipeds having holes therethrough. All outermost surfaces of the first inverted configuration and all outermost surfaces of the second configuration may be mutually exclusive.

[0008] In any embodiment, there may be 12 polyhedra, for example, 8 of the 12 polyhedra are first or second type polyhedra, and correspondingly, 4 of the 12 polyhedra are second or first type polyhedra.

[0009] In any embodiment, the 12 polyhedrons may be connected via the hinges in a repeating order to form the continuous loop, for example, one of the first type polyhedrons, one of the second type polyhedrons, a second of the first type polyhedrons, and so on.

[0010] In any embodiment, each of the first and second polyhedra may be a tetrahedron.

[0011] In any embodiment, each of the first type polyhedra may include four right-angled triangular faces.

[0012] In any embodiment, each of the first and second type polyhedra may have a side length of 1 unit, a square root of 2 units (√(2) units), 2 units, or a square root of 3 units (√(3) units).

[0013] In either embodiment, the continuous loop of polyhedron can be configured between a first inverted configuration and a second inverted configuration, and the first and second inverted configurations can be congruent parallelepipeds having a hole therethrough.

[0014] In either embodiment, all outermost surfaces of the first inverted configuration and all outermost surfaces of the second configuration may be mutually exclusive.

[0015] In either embodiment, the first face of each first type polyhedron and the first and second faces of each second type polyhedron may be congruent.

[0016] In either embodiment, the fourth face of each first type polyhedron and the third and fourth faces of each second type polyhedron may be congruent.

[0017] In either embodiment, each of the twelve polyhedrons may include at least one magnet disposed adjacent each of its faces.

[0018] In either embodiment, the at least one magnet in each polyhedron has an opposite polarity to the at least one magnet in each adjacent polyhedron in the successive loop.

[0019] In any embodiment, each of the first type polyhedra may be a tetrahedron having six sides, including two sides with a side length of 1 unit, two sides with a side length of the square root of 2 units (√(2) units), one side with a side length of 2 units, and one side with a side length of the square root of 3 units (√(3) units).

[0020] In any embodiment, each of the second kind polyhedra may be a tetrahedron having six sides, including two sides with a side length of 1 unit, one side with a side length of the square root of 2 units (√(2) units), one side with a side length of 2 units, and two sides with a side length of the square root of 3 units (√(3) units).

[0021] In any embodiment, any one or more of the above features may be important.

[0022] Exemplary, non-limiting embodiments of the present invention are described with reference to the following drawings, in which like reference numerals refer to like parts throughout the drawings unless otherwise stated. [Brief explanation of the drawings]

[0023] [Figure 1] 1 shows a puzzle with two inverted configurations according to one exemplary embodiment of the present invention. [Figure 2] 1 shows a perspective view of a puzzle according to one exemplary embodiment of the present invention. [Figure 3A] 3 is a schematic representation of the geometry of the first kind polyhedron of the puzzle in Figure 2. [Figure 3B] 3 is a schematic representation of the geometry of the second kind of polyhedron of the puzzle in Figure 2. [Figure 4A] 3 shows a perspective view of a first hinge connection configuration of the puzzle of FIG. 2; FIG. [Figure 4B] 3 shows a perspective view of a second hinge connection configuration of the puzzle of FIG. 2. FIG. [Figure 4C] 3 shows a perspective view of a third hinge connection configuration of the puzzle of FIG. 2; FIG. [Figure 5] Schematic representation of one representative arrangement of magnets in the first and second kind polyhedra of the puzzle of Figure 2. [Figure 6A] 1 shows a top view of a puzzle in an inverted configuration according to one exemplary embodiment of the present invention. [Figure 6B] The front view is shown. [Figure 6C] The right side view is shown. [Figure 6D] The upper right oblique view is shown. [Figure 7A] 1 shows a perspective view of a puzzle in a second configuration according to one exemplary embodiment of the present invention. [Figure 7B] 7B shows a perspective view of the puzzle of FIG. 7A in a third configuration. [Figure 7C]7B shows a perspective view of the puzzle of FIG. 7A in a fourth configuration. [Figure 8A] 1 illustrates a first step in a method for manipulating a puzzle into an inverted configuration according to one exemplary embodiment of the present invention. [Figure 8B] 8B illustrates a second step in the method for manipulating the puzzle of FIG. 8A into an inverted configuration. [Figure 8C] 8B illustrates a third step in the method for manipulating the puzzle of FIG. 8A into an inverted configuration. [Figure 8D] 8B illustrates a fourth step in the method for manipulating the puzzle of FIG. 8A into an inverted configuration. DETAILED DESCRIPTION OF THE INVENTION

[0024] The following describes a hinged magnetic dual geometry puzzle (hereafter referred to as the puzzle for brevity) that includes hinged polyhedrons, each of which has particular geometric properties, and each of which is hinged to other polyhedrons in the puzzle and preferably has structural features that realize unique functions and / or express unique attributes of the puzzle.

[0025] In particular, the puzzles have at least two different types of polyhedral bodies (i.e., have at least two different geometric shapes), a property that provides new and unique attributes that individually and / or jointly enhance the appeal of such puzzles as teaching aids, therapeutic devices, and toys. As will be appreciated from the following description, such attributes may include any one or more of the following: 1. The puzzle has the ability to be configured in one or more ways into a single common polyhedral shape. Each configuration with this common polyhedral shape is called an "inverted configuration" because the puzzle can be flipped (or inverted) from the inside out to form that configuration. Again, the polyhedral shape of each inverted configuration is congruent to the polyhedral shapes of other inverted configurations. In some embodiments, the inverted configuration is a parallelepiped, e.g., a parallelepiped with a hole through it, thus providing a "hole" shape. 2. The ability to realize new configurations that were not previously possible, such as those shown in Figures 1 and 7B-7C. 3. For each inverted configuration, the outermost surface of the puzzle is different from (eg, mutually exclusive with) the outermost surface of the puzzle in each other inverted configuration. 4. For each inverted configuration, the outermost surface of the polyhedron has a different appearance and / or texture (surface treatment) than the outermost surface of at least one other congruent inverted configuration. 5. Geometric and magnetic compatibility with other puzzles allows the puzzle to be assembled and / or combined with other similar puzzles.

[0026] As used herein, the term "congruent" means that two geometries (such as two polyhedra of a single puzzle or the overall shapes of two puzzles) are the same in shape and size. This includes when one geometry is a mirror of another.

[0027] It should be understood that the embodiments described herein are exemplary rather than restrictive, and that the present invention is not limited to the described embodiments. It should also be understood that any embodiment can include any one or more of the features described below in any combination.

[0028] Figure 1 illustrates a dual geometry puzzle 100 according to one exemplary embodiment of the present invention. As described in more detail below, puzzle 100 includes multiple polyhedrons with magnets that form a continuous loop connected to one another via hinges, as described with respect to Figures 2 and 3A-3B. Puzzle 100 is unique because it includes two different types of polyhedrons and magnets that stabilize puzzle 100 in many configurations, such as those shown in Figures 1, 4A-4C, 7A-7C, and 8D.

[0029] 1 shows the same puzzle 100 at two different times, exhibiting a unique "double-flip" attribute, which is its ability to be manipulated into two inverted configurations. As used herein, the term "inverted configuration" refers to a configuration of the puzzle in which the configuration has an overall shape that is congruent with another configuration of the puzzle (i.e., another inverted configuration), but the outermost surfaces of the configuration are mutually exclusive. That is, puzzle 100 can be configured into a single polyhedral shape in two different ways with outermost surfaces that are mutually exclusive.

[0030] For example, puzzle 100 at a first time t1 (designated puzzle 100a) is configured in a first inverted configuration having a parallelepiped shape with a first outermost surface (designated by parallel drawn lines). In contrast, puzzle 100 at a second time t2 (designated puzzle 100b) is configured in a second inverted configuration having a parallelepiped shape that is congruent with the first configuration and exhibits a second outermost surface (designated by cross screen lines).

[0031] The first and second outermost surfaces of puzzle 100 in the first and second flipped configurations (i.e., at time t1 and time t2) are mutually exclusive. In some embodiments, the outermost surfaces of each flipped configuration may have different surface treatments (e.g., graphics and / or textures) to enhance the appeal of the puzzle. For example, the different surface treatments may indicate to a user when different flipped configurations have been implemented.

[0032] Another unique attribute is that the inverted configuration shown in Figure 1 is a parallelepiped with a hole through it, which is balanced and symmetrical, making it visually appealing, suitable for packaging, and a configuration not previously available in known magnetically stabilized puzzles.

[0033] The additional unique attributes of Puzzle 100 will become apparent from the following description.

[0034] The characteristics of puzzle 200 will be described with reference to Figure 2. Puzzle 200 has the same geometric shape as puzzle 100, and therefore can achieve the inverted configuration shown in Figure 1.

[0035] Puzzle 200 includes a plurality of polyhedral modules or polyhedrons 202a-202l connected around loop axis 206 to form a continuous loop. Each polyhedron is a solid body forming a cavity therein and may be formed from a thermoplastic polymer (e.g., PLA) or other rigid material. For clarity, the polyhedrons described herein are not limited to completely solid bodies. In some embodiments, one or more of the polyhedrons may be hollow (i.e., have a cavity) or have one or more cut-outs from their volume.

[0036] The polyhedrons 202a-202l are hinged end-to-end via hinges (e.g., bridge strips 204a-204l) that flexibly join adjacent polyhedrons 202a-202l, thereby enabling reversible switching of the joined bodies so that different faces are adjacent to each other.

[0037] As described below, each of polyhedrons 202a-202l is provided with at least one magnet that stabilizes puzzle 200 into a variety of visually and tactilely appealing configurations, such as the inverted parallelepiped configuration of FIG. 1 and the configurations of FIGS. 7A-7C.

[0038] By manipulating the polyhedrons 202a-202l, the puzzle 200 can be magnetically stabilized into several different configurations. Figures 6A-7C show representative configurations, including a parallelepiped inverted configuration, a cubic hexahedron, a polyhedron with a parallelepiped with two hinged connections, a hexahedron with a triangular outline, various regular polyhedrons, irregular polyhedrons, convex polyhedrons, concave polyhedrons, and other polyhedron types.

[0039] To achieve different configurations, the polyhedrons 202a-202l may be manipulated in a different order in one or more of the following steps or movements. Rotating one or more of the polyhedra 202a-202l about the loop axis 206 (which tends to flip the puzzle 200), Switching one or more polyhedrons 202a-202l around a bridge strip 204a-204l so that different faces of the polyhedrons 202a-202l are adjacent to each other, or One or more polyhedrons 202a to 202l are translated relative to one another.

[0040] Unlike known puzzles, the puzzle of the present invention includes a continuous loop of at least two different polyhedrons 202a-202l. One polyhedron can be constrained to differ from another polyhedron based on any one or more of the following conditions: The two polyhedra have at least one face and / or edge of different size; The two polyhedra have different numbers of faces, edges, and / or vertices; Two polyhedra are geometrically similar but have different face and / or edge sizes, ·Two polyhedra are not congruent, The two polyhedra have different volumes, The two polyhedra have different numbers of isosceles triangular faces, The two polyhedra have different numbers of congruent triangular faces, The two polyhedra have a common polyhedral shape (e.g., both are tetrahedrons) in addition to any one or more of the above criteria.

[0041] Advantageously, by utilizing two or more different polyhedra, puzzle 200 can be manipulated into new and interesting configurations (e.g., those shown in Figures 1 and 6A-7C) and achieve double-inversion functionality.

[0042] It should be understood that the use of different polyhedra complicates the selection of the geometries used for each individual polyhedron. In theory, nearly infinite combinations of different polyhedra can be used. Due to different edge lengths and vertices, most possible combinations of different polyhedra cannot generate harmonious configurations feasible with puzzle 200. For example, the parallelepiped shape with a through hole of FIG. 1 cannot be realized if all polyhedra are congruent, or if a single polyhedron has most geometries other than those described below in FIGS. 3A-3B. Furthermore, puzzle 200 cannot achieve the double-inversion function with inverted configurations of the same parallelepiped with most other geometries. Furthermore, due to inconsistent faces and edges, most combinations of other polyhedra cannot achieve the combinations of configurations shown in FIGS. 7A-7C. As described below, puzzle 200 includes multiple polyhedra of different types, but the different types share some common characteristics, such as common edge lengths and some congruent faces. These common attributes allow the puzzle as a whole to achieve the configurations described herein.

[0043] Thus, a key technical problem overcome by the puzzles described herein is to create a puzzle that can achieve popular magnetically stabilized configurations and double-reversal functionality by having a selection and ordered arrangement of magnetized polyhedra having two or more different geometries. It should be appreciated that puzzles with polyhedra of different geometries present the challenge of inconsistent edges and faces (i.e., different edge lengths and face shapes), which makes it even more difficult to create a puzzle that can achieve popular magnetically stabilized configurations.

[0044] In the illustrated embodiment, puzzle 200 is formed by a continuous loop of twelve hinged polyhedrons 202a-202l, each of which is a tetrahedron. Each tetrahedron is hingedly connected to two adjacent tetrahedrons along loop axis 206 via two of bridge strips 204a-204l.

[0045] Eight of the twelve polyhedra 202a, 202c, 202d, 202f, 202g, 202i, 202j, and 202l are first-type tetrahedra having a first geometric shape as shown in FIG. 3A. The remaining four polyhedra 202b, 202e, 202h, and 202k are second-type tetrahedra having a different second geometric shape as shown in FIG. 3B. As used herein, when two or more polyhedra are congruent to one another, they may be a single type of polyhedron (i.e., first type or second type) despite any differences in surface treatment. For example, two mirror polyhedra may both be first-type or second-type polyhedra because they are congruent.

[0046] The polyhedra 202a-202l are hinged in a repeating sequence of one of the first type, one of the second type, and another of the first type. That is, if the first type polyhedra are designated as type "A" and the second type polyhedra are designated as type "B," the polyhedra 202a-202l are connected in the following order, starting with the tetrahedron 202a: A, B, A, A, B, A, A, B, A, A, B, A, B. Thus, the puzzle 200 may include (consist of), for example, eight first type polyhedra and four second type polyhedra.

[0047] 3A and 3B show the geometries of the first-type and second-type polyhedra 202a-202l of the puzzle 200, respectively. The meaning of FIGS. 3A and 3B is illustrated by an example diagram 208 illustrating the relationship between different edge lengths of the first-type and second-type polyhedra. Edges marked with a plus sign ("+") have a length of one unit, which can be scaled up or down depending on the scale used in different embodiments. Regardless of the value of the unit ("+"), the relative relationship between different edges remains constant across different embodiments. That is, regardless of the value of the unit length ("+"), edges marked with a "circle" have an edge length equal to √(2) (i.e., the square root of two times the unit length), edges marked with a "Δ" have an edge length equal to 2 (i.e., the square root of three times the unit length), and edges marked with a "square" have an edge length equal to √(3) (i.e., the square root of three times the unit length).

[0048] 3A schematically illustrates the geometry of a first-kind polyhedron 202a that is congruent with polyhedrons 202c, 202d, 202f, 202g, 202i, 202j, and 202l. As illustrated, polyhedron 202a is a tetrahedron having four faces 210, 212, 214, and 216 and six sides 218, 220, 222, 224, 226, and 228. The relative lengths of each side are indicated by an example diagram 208. Due to the relationship of the side lengths in example diagram 208, all four faces 210, 212, 214, and 216 are right-angled triangles, and second face 212 and third face 214 are isosceles triangles.

[0049] In the illustrated embodiment, each of the first type polyhedra is a six-sided tetrahedron including two edges (edges 218 and 228) with edge lengths of 1 unit, two edges (edges 224 and 226) with edge lengths of √(2) units, one edge (edge ​​222) with edge lengths of 2 units, and one edge (edge ​​220) with edge lengths of √(3) units.

[0050] 3B schematically illustrates the geometry of a second-kind polyhedron 202b that is congruent with polyhedrons 202e, 202h, and 202k. As illustrated, polyhedron 202b is a tetrahedron having four faces 230, 232, 234, and 236 and six sides 238, 240, 242, 244, 246, and 248. The relative lengths of each side are indicated by diagram 208. Based on the side-length relationships in diagram 208, all four faces 230, 232, 234, and 236 are right-angled triangles. Furthermore, first face 230 and second face 232 are congruent, and third face 234 and fourth face 236 are congruent.

[0051] In the illustrated embodiment, each of the second type polyhedra is a six-sided tetrahedron, including two sides (sides 238 and 244) with a side length of 1 unit, one side (side 248) with a side length of √(2) units (the square root of 2 units), one side (side 242) with a side length of 2 units, and two sides (sides 240 and 246) with a side length of √(3) units (the square root of 3 units).

[0052] Comparing Figure 3A with Figure 3B, it is clear that the first face 210 of the first-type polyhedron 202a and the first and second faces 230 and 232 of the second-type polyhedron 202b are congruent. This congruence, along with the relationship of the other edges of the two types of tetrahedrons, the order of the first and second types of polyhedrons in the continuous loop, and the hinge arrangement, allows the first face 210 of one of the first-type polyhedrons to be adjacent to the first face 230 or the second face 232 of one of the second-type polyhedrons, forming an arrangement with three orthogonal faces. Such an arrangement with three orthogonal faces is useful for the construction of various parallelepiped configurations (e.g., the inverted parallelepiped configuration of Figure 1, the cuboid of Figure 7A, and the hinged parallelepiped of Figure 7B).

[0053] 4A-4C, we will now describe in detail exemplary hinge arrangements between the polyhedrons of puzzle 200. The exemplary embodiment includes bridge strips in three different types of locations (the different edges identified below correspond to the illustrations in FIGS. 3A-3B). between a first edge of a tetrahedron of the first kind and a first edge of an adjacent tetrahedron of the second kind (FIG. 4A shows a bridge strip 204a extending from the first edge 218 of the (first kind) polyhedron 202a to the first edge 238 of the (second kind) polyhedron 202b); between the first edge of a tetrahedron of the first kind and the fourth edge of an adjacent tetrahedron of the second kind (FIG. 4B shows a bridge strip 204B extending from the first edge 218 of the (first kind) polyhedron 202c to the fourth edge 244 of the (second kind) polyhedron 202b), and Between the fifth edge of a first-type tetrahedron and the fifth edge of an adjacent first-type tetrahedron (FIG. 4C shows a bridge strip 204c extending from the fifth edge 226 of a (first-type) polyhedron 202c to the fifth edge 226 of an adjacent (first-type) polyhedron 202d).

[0054] In some embodiments, the aforementioned hinge types are arranged around the puzzle 200 in the order described above with respect to the puzzle 200 of FIG. 2. In some embodiments, the bridge strips may be adhesive, decal, or tape-type bridge strips adhesively bonded to adjacent faces of the polyhedrons. However, bridge strips are not limited thereto. In some embodiments, the bridge strips are internal bridge strips that extend through the interior volume of each polyhedron.

[0055] Despite the exemplary hinges shown in Figures 2-4C, hinges can take many different forms. In some embodiments, as shown in Figure 2, each of the hinges is a decal or sticker applied to the faces of at least two adjacent polyhedrons such that the hinge extends directly from one of the polyhedrons to another. While each hinge in Figure 2 connects two adjacent polyhedrons, in some embodiments, one or more hinges may connect two or more polyhedrons. For example, in some embodiments, a single continuous decal can be applied to two or more polyhedrons. Exemplary hinges of this configuration are described in detail in U.S. Patents Nos. 10,569,185 and 10,918,964 to Hoenigschmid, which are incorporated herein by reference in their entireties.

[0056] In other embodiments, the hinge is integrally formed with the polyhedron module (e.g., a living hinge) and extends directly from one of the modules to an adjacent module. In such embodiments, the hinge may be formed as a flexible polymer strip of the same or similar material as the housing of the polyhedron module. Exemplary hinges of this configuration are described in detail in U.S. Patent No. 11,358,070 to Aberg, which is incorporated herein by reference in its entirety.

[0057] In other embodiments, the hinges are formed as one or more internal flexible connecting strips (e.g., thin flexible polymers or fabrics) that extend between adjacent modules and are configured to be secured within the lumens of the adjacent polyhedrons. Exemplary hinges of this configuration are described in detail in PCT Publication WO 2022 / 130285 to Hoenigschmid, which is incorporated herein by reference in its entirety.

[0058] In any embodiment, multiple hinges may extend between adjacent sides of adjacent modules. The above hinge structures are exemplary and not limiting.

[0059] 5, some or all of the polyhedrons of puzzle 200 include magnets that stabilize puzzle 200 in any one or more of the configurations shown and described herein, including the inverted configuration of FIG. 1 and the configurations of FIGS. 7A-7C. In particular, at least one magnet is disposed on each polyhedron at one location and has a polarity that is magnetically coupled to at least one magnet of the opposite polarity that is disposed on another polyhedron, such as when puzzle 200 is manipulated into a different configuration.

[0060] In the exemplary embodiment, each face of each polyhedron includes at least one magnet disposed adjacent thereto, i.e., each first type polyhedron (e.g., tetrahedron 202a) includes at least one magnet 250a disposed adjacent to first face 210, at least one magnet 250b disposed adjacent to second face 212, at least one magnet 250c disposed adjacent to third face 214, and at least one magnet 250d disposed adjacent to fourth face 216.

[0061] Similarly, each second type polyhedron (e.g., tetrahedron 202b) includes at least one magnet 252a positioned adjacent to first face 230, at least one magnet 252b positioned adjacent to second face 232, at least one magnet 252c positioned adjacent to third face 234, and at least one magnet 252d positioned adjacent to fourth face 236.

[0062] In exemplary embodiments, each magnet is embedded in a respective face, e.g., embedded in a recess (external or internal) formed in the face itself. In other embodiments, each magnet can be positioned within the internal cavity of each polyhedron and can be positioned sufficiently close to the associated face so that the magnetic flux of the magnet extends through the face. For example, in some embodiments, each magnet may be held within a groove, slot, and / or track within the internal cavity. In some embodiments, one or more of the magnets can be positioned within brackets (e.g., brackets located near the vertices of the sides of the polyhedron) so that the magnetic flux from the magnet extends through multiple faces of the polyhedron. Exemplary structures for securing magnets to polyhedrons are described in U.S. Patents Nos. 10,569,185 and 10,918,964 to Hoenigschmid, and U.S. Patent Publication No. US 2022 / 0047960, which are incorporated herein by reference.

[0063] Magnets 250a-250d and 252a-252d are positioned and polarized to magnetically couple with other magnets in puzzle 200. For example, in any embodiment, any one or more of the following pairs of magnets may be positioned and polarized to magnetically couple with each other (i.e., the two magnets may have opposite polarities): A magnet 250a positioned adjacent to the first face 210 of the first kind of polyhedron and a magnet 252a positioned adjacent to the first face 230 of the second kind of polyhedron (e.g., a hinged second kind of polyhedron). A magnet 250a positioned adjacent to the first face 210 of the first kind of polyhedron and a magnet 252b positioned adjacent to the second face 232 of the second kind of polyhedron (e.g., a hinged second kind of polyhedron). A magnet 250b positioned adjacent to the second face 212 of an adjacent first kind polyhedron (eg, a hinged first kind polyhedron). A magnet 250c positioned adjacent to the third face 214 of an adjacent first kind polyhedron (eg, a hinged first kind polyhedron). · A magnet 250d positioned adjacent to the fourth face 216 of the first kind polyhedron. A magnet 252c positioned adjacent to the third face 234 of the second kind polyhedron. · A magnet 252d positioned adjacent to the fourth face 236 of the second kind polyhedron.

[0064] To facilitate the magnetic coupling described above, in some embodiments, each first-type polyhedron has a similarly positioned magnet 250a-250d, and each second-type polyhedron has a similarly positioned magnet 252a-252d. In some embodiments (such as shown in FIG. 2), each polyhedron has magnets of a single polarity (i.e., positive or negative), with the polarity alternating between successive polyhedrons in a successive loop, regardless of whether the polyhedron is of the first or second type. That is, in some embodiments, the polarity of all magnets in one polyhedron is either positive or negative, and the polarity of all magnets in the next polyhedron in the successive loop is correspondingly opposite, i.e., either negative or positive.

[0065] In some embodiments, each of the first type polyhedrons and each of the second type polyhedrons has four magnets. However, in some embodiments, one or more of the first type polyhedrons and / or one or more of the second type polyhedrons has fewer than four magnets, such as one, two, or three magnets. Advantageously, including fewer magnets can reduce the manufacturing costs of the puzzle, even at the expense of reduced magnetic stability.

[0066] FIGS. 6A-6D show diagrams of puzzle 600 in one of the inverted configurations shown in FIG. 1. Puzzle 600 is identical to puzzle 100 of FIG. 1, and puzzle 600 includes polyhedrons in the same hinged arrangement with the same geometry as shown in FIGS. 2 and 3A-3B. In particular, FIGS. 6A-6D show plan, front, right side, and top perspective views, respectively, of the parallelepiped inverted configuration shown in puzzle 100a of FIG. 1. As shown, puzzle 600 is magnetically stabilized in a parallelepiped configuration with a square hole 664 extending completely through it. Magnetically stabilized puzzles with such a geometry were not previously known. Thus, the geometry of puzzle 600, together with the magnets installed in the polyhedron, provides valuable new functionality not previously realized.

[0067] The hole 664 is formed by the different geometric shapes between the first type polyhedron and the second type polyhedron. For example, polyhedrons 602a and 602b are connected to each other and have different geometric shapes. That is, polyhedron 602a is the first type polyhedron shown in FIG. 3A, and 602b is the second type polyhedron shown in FIG. 3B. The same is true for polyhedrons 602g and 602h. The different edge lengths between the first type polyhedron and the second type polyhedron form the hole 664.

[0068] 7A-7C show additional magnetic stabilization configurations that can be achieved using a puzzle 700 that includes a polyhedron having the same geometry as puzzle 100 of FIG. 1, in the same hinged arrangement, and having the same geometry as shown in FIGS. 2 and 3A-3B.

[0069] One interesting attribute of puzzle 100 is that all such configurations share a common volume. The configurations shown in Figures 7A-7C represent, but are not limited to, the interesting configurations possible with dual geometry puzzle 700. Many additional magnetically stable configurations can be realized with puzzle 100.

[0070] FIG. 7A illustrates a cubic hexahedron or cubic parallelepiped polyhedron that can be implemented in puzzle 100. The cubic hexahedron configuration is ideal for packaging and shipping puzzle 100 given its conformity and compact size. Interestingly, puzzle 700 includes polyhedra with at least two different geometries, but can realize the cubic hexahedron of FIG. 7A because only first-type polyhedra are present in the configuration shown in FIG. 7A. That is, in the configuration of FIG. 7A, the outer surface is composed of congruent first-type polyhedra 702a, 702c, 702d, 702f, 702g, 702i, 702j, and 702l.

[0071] FIG. 7B shows a magnetically stable polyhedron of two congruent hinged parallelepipeds, which can be realized in puzzle 100.

[0072] Figure 7C is another magnetically stable hexahedron with a triangular outline, which can be achieved in a magnetically stable position by two sequential moves from the cubic hexahedron of Figure 7A.

[0073] Figures 8A-8D illustrate an exemplary method (particularly for puzzle 100a) of manipulating puzzle 800 of the present invention into the parallelepiped inverted configuration shown in Figure 1. Puzzle 800 has the same geometry as puzzle 100 of Figure 1, and puzzle 800 includes polyhedra in the same hinged arrangement and having the same geometry as shown in Figures 2 and 3A-3B.

[0074] To further guide the user, the polyhedrons of puzzle 800 correspond to the polyhedrons of Figure 2. That is, polyhedron 802a of Figure 8A corresponds to polyhedron 202a of Figure 2, polyhedron 802b of Figure 8B corresponds to polyhedron 202b, and so on.

[0075] The following description provides a general method for constructing puzzle 800 as a parallelepiped inverted configuration, i.e., the parallelepiped inverted configuration shown in Figures 1 and 6A-6D. Experienced users will understand that by modifying the method described below, congruent inverted configurations of the outermost surfaces that are mutually exclusive can be achieved.

[0076] It should be understood that the exemplary method is representative and not limiting, and the inverted configuration shown in Figure 8D may be achieved by combining fewer and / or some of the steps illustrated.

[0077] In an optional first step shown in FIG. 2, the puzzle 800 is arranged in an exemplary open-loop configuration.

[0078] 8A, opposing polyhedrons having different geometries are then positioned adjacent to one another (and magnetically stabilized relative to one another) such that puzzle 800 is oriented in a linear configuration generally represented by longitudinal axis 858. For example, polyhedron 802j (first type polyhedron) is positioned adjacent to polyhedron 802k (second type polyhedron), polyhedron 802a (first type polyhedron) is positioned adjacent to polyhedron 802h (second type polyhedron), and so on.

[0079] It should be noted that a user can adjust the above steps to change which outermost faces are represented in the resulting parallelepiped configuration of FIG. 8D. That is, when puzzle 800 is manipulated into the parallelepiped of FIG. 8D by placing puzzle 800 in the configuration shown in FIG. 8A, where polyhedron 802a is placed adjacent to polyhedron 802h, it will exhibit a first outermost surface. However, when manipulated into the parallelepiped of FIG. 8D by instead placing polyhedron 802l (a polyhedron of the first kind) adjacent to polyhedron 802e (a polyhedron of the second kind), puzzle 800 will exhibit a second outermost surface, the second outermost surface and the first outermost surface being mutually exclusive. Such a modification allows a user to realize two parallelepiped-inverted configurations, thereby realizing the double-inversion functionality of puzzle 800. Thus, puzzle 800 can achieve the same shape (shown in FIG. 1) with two different appearances if the first outermost surface has a different appearance than the second outermost surface.

[0080] Returning to Figure 8A, the end polyhedra are rotated inward until they are hinged to the corresponding penultimate polyhedron. In the illustrated example, polyhedra 802j and 802k are rotated inward onto polyhedra 802i and 802l, respectively. Similarly, polyhedra 802d and 802e are rotated inward, respectively. This results in the configuration shown in Figure 8B.

[0081] 8B, in this intermediate configuration, puzzle 800 is generally represented by a vertical axis 858 and a horizontal axis 860 perpendicular thereto. On each side of vertical axis 858, puzzle 800 has three representation points (one center point and two outer points) that comprise the vertices of one or more polyhedra. Next, the polyhedra are manipulated so that the center point on a first side of vertical axis 858 intersects with an outer point on a first side of horizontal axis 860. For example, the points of polyhedra 802b, 802c are brought together in the first "quadrant" of axes 858, 860. Furthermore, the polyhedra are manipulated so that the center point on a second side (opposite the first side) of vertical axis 858 intersects with an outer point on a second side (opposite the first side) of horizontal axis 860. For example, the points of polyhedra 802h and 802i are brought together in a second "quadrant" diagonal to the first, resulting in the configuration shown in Figure 8C.

[0082] 8C, the central portion of puzzle 800 (where axes 858, 860 intersect) is lifted upward while simultaneously rotating the outermost points downward. For example, polyhedrons 802a and 802h may be raised while rotating downward the points formed by polyhedrons 802e, 802k. Due to the geometry of puzzle 800, this movement ultimately and naturally rotates polyhedrons 802a, 802h in opposite directions along lateral axis 860, causing them to move away from each other. Thus, puzzle 800 achieves the inverted parallelepiped configuration of FIG. 8D.

[0083] FIG. 8D shows the parallelepiped inverted configuration generated by the above steps. The configuration in FIG. 8D is the same as the configuration shown in FIGS. 1 and 6A-6D. As shown, puzzle 800 has a hole 864 running through it. The hole 864 is a result of the different geometries between the first and second polyhedra. For example, polyhedra 802a and 802b are connected to each other at hinge 804a and have different geometries. That is, polyhedron 802a is the first polyhedron shown in FIG. 3A, and polyhedron 802b is the second polyhedron shown in FIG. 3B. The same is true for polyhedra 802g and 802h. Therefore, the different edge lengths between the first and second polyhedrons form the hole 864.

[0084] The above considered features combine to give the puzzle numerous unique properties that enhance its appeal as a puzzle, toy, and / or educational aid for learning geometry and other mathematical concepts. As an example, hinge connections between adjacent polyhedrons allow puzzle 200 to be flipped from inside out about loop axis 206. The hinge connections in successive loops allow for rapid manipulation between various configurations without losing a single polyhedron.

[0085] The specific geometry, regular arrangement, and positioning of the magnetized polyhedrons allows the puzzle to achieve many magnetically stable configurations that are visually and tactilely appealing, including, but not limited to, the configurations shown in Figures 1, 6A-6D, 7A-7C, and 8D. The configurations exhibit unique symmetrical forms and can be quickly rearranged, for example, into the cubic configuration of Figure 7A for convenient packaging, storage, and portability. In particular, the use of two different types of polyhedrons with the specific geometries defined in Figures 3A and 3B is novel and non-obvious.

[0086] Finally, the puzzle is stabilized by specific configuration alignments and polarizing magnets in all key configurations, giving it a delightful sense of solid quality.

[0087] It should be understood that the above benefits may be achieved by any single feature or by any non-obvious combination of the features.

[0088] Representative embodiments of the present invention may be embodied in many different forms and are not limited to the embodiments set forth herein, but rather the purpose of providing these embodiments is to provide a more thorough and complete disclosure of the present invention.

[0089] It should be noted that when one component is considered to be "connected" to another component, it may be directly connected to the other component or there may be intervening components. As used herein, the terms "top," "bottom," "side," "vertical," "horizontal," "left," "right," and similar expressions are used for illustrative purposes only.

[0090] Unless otherwise limited, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art. The terms used to describe the present invention herein are for the purpose of describing specific examples only and are not intended to limit the present invention. As used herein, the term "and / or" includes any and all combinations of the associated listed items.

Claims

1. A double geometry puzzle, a continuous loop of 12 polyhedrons connected to each other via hinges; eight of the twelve polyhedrons are first kind polyhedrons having a first geometric shape and four of the twelve polyhedrons are second kind polyhedrons having a different second geometric shape, each of the twelve polyhedrons including at least one magnet disposed proximate at least one face thereof; A dual geometry puzzle, wherein the continuous loop of the polyhedron is configurable between a first inverted configuration and a second inverted configuration, the first and second inverted configurations being congruent parallelepipeds having a hole therethrough.

2. 2. The dual geometry puzzle of claim 1, wherein all outermost surfaces of the first inverted configuration and all outermost surfaces of the second inverted configuration are mutually exclusive.

3. 2. The dual geometry puzzle of claim 1, wherein the 12 polyhedra are connected via the hinges in a repeating order of one first type polyhedron, one second type polyhedron, and a second first type polyhedron, thereby forming the continuous loop.

4. 2. The dual geometry puzzle of claim 1, wherein each of the first kind of polyhedron and the second kind of polyhedron is a tetrahedron.

5. 2. The dual geometry puzzle of claim 1, wherein each of said first kind polyhedra includes four right triangular faces.

6. 2. The dual geometry puzzle of claim 1, wherein each of the first and second polyhedra has a side length of 1 unit, √(2) units, which is the square root of 2 units, √(3) units, which is the square root of 2 units, or √(3) units, which is the square root of 3 units.

7. 2. The dual geometry puzzle of claim 1, wherein a first face of each of the first kind polyhedra and a first and second face of each of the second kind polyhedra are congruent.

8. 8. The dual geometry puzzle of claim 7, wherein the fourth face of each of the first kind polyhedrons and the third and fourth faces of each of the second kind polyhedrons are congruent.

9. 2. The dual geometry puzzle of claim 1, wherein each of the twelve polyhedrons includes at least one magnet disposed adjacent each of its faces.

10. 2. The dual geometry puzzle of claim 1, wherein each of the first kind polyhedra is a tetrahedron having six sides, the six sides including two sides having a side length of 1 unit, two sides having a side length of √(2) units, which is the square root of 2 units, one side having a side length of 2 units, and one side having a side length of √(3) units, which is the square root of 3 units.

11. 11. The dual geometry puzzle of claim 10, wherein each of the second kind polyhedra is a tetrahedron having six sides, the six sides including two sides with a side length of 1 unit, one side with a side length of √(2) units, which is the square root of 2 units, one side with a side length of 2 units, and two sides with a side length of √(3) units, which is the square root of 3 units.

12. 4. The dual geometry puzzle of claim 3, wherein the first face of each of the first kind polyhedra and the first and second faces of each of the second kind polyhedra are congruent.

13. 13. The dual geometry puzzle of claim 12, wherein each of the first kind polyhedra is a tetrahedron having six sides, the six sides including two sides having a side length of 1 unit, two sides having a side length of √(2) units, which is the square root of 2 units, one side having a side length of 2 units, and one side having a side length of √(3) units, which is the square root of 3 units.

14. A double geometry puzzle, a continuous loop of 12 polyhedrons connected to each other via hinges; eight of the twelve polyhedrons are first kind polyhedrons having a first geometric shape and four of the twelve polyhedrons are second kind polyhedrons having a different second geometric shape, each of the twelve polyhedrons including at least one magnet disposed proximate at least one face thereof; A dual geometry puzzle, wherein a first face of each of the first kind polyhedra and a first face and a second face of each of the second kind polyhedra are congruent.

15. 15. The dual geometry puzzle of claim 14, wherein the fourth face of each of the first kind polyhedrons and the third and fourth faces of each of the second kind polyhedrons are congruent.

16. 16. The dual geometry puzzle of claim 15, wherein the 12 polyhedra are connected via the hinges in a repeating order of one polyhedron of the first kind, one polyhedron of the second kind, a second polyhedron of the first kind, and so on, to form the continuous loop.

17. 15. The dual geometry puzzle of claim 14, wherein the twelve polyhedra are connected via the hinges in a repeating order of one polyhedron of the first kind, one polyhedron of the second kind, a second polyhedron of the first kind, and so on, to form the continuous loop.

18. 18. The dual geometry puzzle of claim 17, wherein each of the first and second polyhedra has a side length of 1 unit, √(2) units which is the square root of 2 units, √(3) units which is the square root of 2 units, or √(3) units which is the square root of 3 units.

19. 18. The dual geometry puzzle of claim 17, wherein each of the first kind polyhedra is a tetrahedron having six sides, the six sides including two sides having a side length of 1 unit, two sides having a side length of √(2) units, which is the square root of 2 units, one side having a side length of 2 units, and one side having a side length of √(3) units, which is the square root of 3 units.

20. the fourth face of each of the first kind polyhedrons and the third and fourth faces of each of the second kind polyhedrons are congruent; 15. The dual geometry puzzle of claim 14, wherein each of the first and second polyhedra has a side length of 1 unit, √(2) units which is the square root of 2 units, √(3) units which is the square root of 2 units, or √(3) units which is the square root of 3 units.

21. 15. The dual geometry puzzle of claim 14, wherein each of the first kind polyhedra is a tetrahedron having six sides, the six sides including two sides having a side length of 1 unit, two sides having a side length of √(2) units, which is the square root of 2 units, one side having a side length of 2 units, and one side having a side length of √(3) units, which is the square root of 3 units.

22. 22. The dual geometry puzzle of claim 21, wherein each of the second kind polyhedra is a tetrahedron having six sides, the six sides including two sides with a side length of 1 unit, one side with a side length of √(2) units, which is the square root of 2 units, one side with a side length of 2 units, and two sides with a side length of √(3) units, which is the square root of 3 units.

23. the continuous loop of polyhedron is configurable between a first inverted configuration and a second inverted configuration, the first inverted configuration and the second inverted configuration being congruent parallelepipeds having a hole therethrough; 15. The dual geometry puzzle of claim 14, wherein all outermost surfaces of the first inverted configuration and all outermost surfaces of the second inverted configuration are mutually exclusive.

24. 24. The dual geometry puzzle of claim 23, wherein the twelve polyhedra are connected via the hinges in a repeating order of one polyhedron of the first kind, one polyhedron of the second kind, a second polyhedron of the first kind, and so on, to form the continuous loop.

25. 15. The dual geometry puzzle of claim 14, wherein each of the first kind of polyhedron and the second kind of polyhedron is a tetrahedron.

26. 15. The dual geometry puzzle of claim 14, wherein each of the first kind polyhedra includes four right triangular faces.

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