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 constructed in different geometric configurations, for example, as shown in British Patent Application GB2,107,200 to Asano and U.S. Patent No. 6,264,199B1 to Schaedel. As taught in the prior art, the attributes of any particular polyhedral puzzle are highly dependent on the geometry and hinge connection configuration of that particular puzzle. For example, the folding puzzle taught in Schaedel consists of 24 identical isosceles tetrahedral bodies formed by four triangular faces with angles of approximately 70.53°, 54.74°, and 54.74°. The tetrahedrons are joined together 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 faces and edges of the polyhedrons, 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, and 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 polyhedral 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 are configured to be manipulated around the loop axis of the continuous loop (i.e., flipping the puzzle from inside out) and / or switched around 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). Also, multiple magnets with complementary polarity are configured in the entire puzzle. Advantageously, the magnets stabilize the puzzle into many configurations.

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

[0007] In another aspect, the present invention provides a dual geometry puzzle comprising a continuous loop of polyhedrons connected to one another via hinges, a first plurality of polyhedrons being of a first kind having a first geometric shape and a second plurality of polyhedrons being of a second kind having a different second geometric shape, each of the polyhedrons including at least one magnet disposed proximate to at least one face thereof. The continuous loop of polyhedrons 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 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 of the polyhedra. For example, 8 of the 12 polyhedra are first type or second type polyhedra, and correspondingly, 4 of the 12 polyhedra are second type or first type polyhedra.

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

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

[0011] In any embodiment, each of the first type polyhedrons 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, the square root of 2 units (√(2) units), 2 units, or the 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 inverted configuration and the second inverted configuration can be congruent parallelepipeds having a hole therethrough.

[0014] In either embodiment, all of the outermost surfaces of the first inverted configuration and all of the 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 any 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 polyhedrons may be a tetrahedron having six sides, including two sides having a side length of 1 unit, two sides having a side length of the square root of 2 units (√(2) units), one side having a side length of 2 units, and one side having a side length of the square root of 3 units (√(3) units).

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

[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 various drawings unless otherwise stated, and in which: [Brief description of the drawings]

[0023] [Figure 1] 1 shows a puzzle in two inverted configurations according to one exemplary embodiment of the present invention. [Diagram 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 geometric shape of a polyhedron of the first kind in the puzzle of FIG. 2. [Figure 3B] 3 is a schematic representation of the geometry of a polyhedron of the second kind in the puzzle of FIG. 2. [Figure 4A] FIG. 3 shows a perspective view of a first hinge connection arrangement of the puzzle of FIG. 2. [Figure 4B] FIG. 3 shows a perspective view of a second hinge connection arrangement of the puzzle of FIG. 2. [Figure 4C] FIG. 3 shows a perspective view of a third hinge connection configuration of the puzzle of FIG. 2 . [Diagram 5] 3 is a schematic representation of one representative arrangement of magnets in the first and second kind polyhedra of the puzzle of FIG. 2. [Figure 6A] FIG. 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 of manipulating the puzzle of FIG. 8A into a flipped configuration. [Figure 8C] 8B illustrates a third step in the method of manipulating the puzzle of FIG. 8A into an inverted configuration. [Figure 8D] 8B illustrates a fourth step in the method of manipulating the puzzle of FIG. 8A into an inverted configuration. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0024] The following describes a hinged magnetic dual geometry puzzle (for brevity, hereafter referred to as the puzzle) that includes hinged polyhedrons, each of which has specific geometric properties, and each of which is preferably hinged to other polyhedrons in the puzzle and 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 realizes new and unique attributes that individually and / or collectively 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 get to that configuration. Again, the polyhedral shape of each inverted configuration is congruent to the polyhedral shapes of the 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 (e.g., mutually exclusive) from 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 geometric figures (such as two polyhedra of a single puzzle, or the overall shapes of two puzzles) are the same in shape and size. This includes cases where one geometric figure is the mirror of another.

[0027] It should be understood that the embodiments described herein are representative rather than limiting, and that the present invention is not limited to the embodiments described. 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 in accordance with 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 a number of configurations, such as those shown in Figures 1, 4A-4C, 7A-7C, and 8D.

[0029] In particular, Figure 1 shows the same puzzle 100 at two different times, exhibiting a unique "double-flip" attribute, which is the ability to be manipulated into two inverted configurations. As used herein, the term "inverted configuration" refers to a configuration of a puzzle that has a congruent overall shape with another configuration of the puzzle (i.e., another inverted configuration), but the outermost surface of the configuration is mutually exclusive with the outermost surface of the other configuration. 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 as puzzle 100a) is configured in a first inverted configuration having a parallelepiped shape with a first outermost surface (designated by the parallel drawn lines). In contrast, puzzle 100 at a second time t2 (designated as puzzle 100b) is configured in a second inverted configuration having a parallelepiped shape that is congruent to the first configuration and exhibits a second outermost surface (designated by the 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 surface of each flipped configuration may have a different surface treatment (e.g., graphics and / or texture) to enhance the appeal of the puzzle. For example, the different surface treatments may indicate to a user when a different flipped configuration has been implemented.

[0032] Another unique attribute is that the inverted configuration shown in Figure 1 is a parallelepiped with a hole passing 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] Additional unique attributes of Puzzle 100 will become apparent from the following description.

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

[0035] The puzzle 200 includes a number of polyhedral modules or polyhedrons 202a-202l connected around a 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) and / 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 to allow reversible switching of the joined bodies such that different faces are adjacent to each other.

[0037] As described below, each polyhedron 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 a number of different configurations. Figures 6A-7C show representative configurations including a parallelepiped inverted configuration, a cubic hexahedron, a polyhedron having a parallelepiped with two hinge 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 during 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 such that different faces of the polyhedrons 202a-202l are adjacent to each other, or One or more of the polyhedrons 202a-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 distinct polyhedrons 202a-202l. One polyhedron can be constrained to be different 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 tetrahedral) in addition to any one or more of the above criteria.

[0041] Advantageously, through the use of two or more different polyhedra, puzzle 200 can be manipulated into new and interesting configurations (eg, those shown in Figures 1 and 6A-7C) to achieve double inversion functionality.

[0042] It should be appreciated that the use of different polyhedra complicates the selection of the geometry used for each individual polyhedron. In theory, an almost infinite combination of different polyhedra can be used. Due to the different edge lengths and vertices, most possible combinations of different polyhedra cannot generate harmonious configurations that are feasible with puzzle 200. For example, the parallelepiped shape with through holes 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. Also, puzzle 200 cannot realize 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 realize the combination of configurations shown in FIGS. 7A-7C. As described below, puzzle 200 includes multiple polyhedra of different types, but the different types of polyhedra share some common characteristics, such as common edge lengths and some congruent faces. These common attributes allow the puzzle as a whole to realize the configurations described herein.

[0043] Thus, a significant technical problem overcome by the puzzles described herein is to have a selection and ordered arrangement of magnetized polyhedra having two or more different geometries to provide a puzzle that can achieve popular magnetically stabilized configurations and double inversion functionality. It should be appreciated that puzzles having 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 provide a puzzle that can achieve popular magnetically stabilized configurations.

[0044] In the illustrated embodiment, the 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 a loop axis 206 via two of the bridge strips 204a-204l.

[0045] Eight of the twelve polyhedra 202a, 202c, 202d, 202f, 202g, 202i, 202j, 202l are first type tetrahedrons having a first geometric shape as described in FIG. 3A. The remaining four polyhedra 202b, 202e, 202h, 202k are second type tetrahedrons having a different second geometric shape as described in FIG. 3B. As used herein, when two or more polyhedra are congruent with each other, 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 polyhedrons because they are congruent.

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

[0047] 3A and 3B show the geometry of the first and second type polyhedra 202a-202l of the puzzle 200, respectively. The meaning of FIG. 3A and FIG. 3B is illustrated by an example diagram 208 illustrating the relationship of different side lengths of the first type polyhedron and the second type polyhedron. The sides marked with a plus sign "+" have a length of one unit that can be expanded or contracted depending on the scaling in different embodiments. Regardless of the value of the unit ("+"), the relative relationship between the different sides remains constant among different embodiments. That is, regardless of the numerical value of the unit length "+", the sides marked with "o" have a side length equal to √(2)(unit length) (i.e., the square root of two times the unit length), the sides marked with "Δ" have a side length equal to 2(unit length), and the sides marked with "□" have a side length equal to √(3)(unit length) (i.e., the square root of three times the unit length).

[0048] 3A shows a schematic representation of the geometry of a first kind polyhedron 202a that is congruent with polyhedrons 202c, 202d, 202f, 202g, 202i, 202j, and 202l. As shown, 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 shown by an example diagram 208. Due to the relationship of the side lengths in the example diagram 208, the four faces 210, 212, 214, and 216 are all right triangles, and the second face 212 and the 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) having an edge length of 1 unit, two edges (edges 224 and 226) having an edge length of √(2) units, one edge (edge ​​222) having an edge length of 2 units, and one edge (edge ​​220) having an edge length of √(3) units.

[0050] 3B shows a schematic diagram of the geometry of a second kind of polyhedron 202b that is congruent with the polyhedrons 202e, 202h, and 202k. As shown, the 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 shown by the example diagram 208. According to the side length relationships in the example diagram 208, the four faces 230, 232, 234, and 236 are all right-angled triangles. In addition, the first face 230 and the second face 232 are congruent, and the third face 234 and the 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 Fig. 3A with Fig. 3B, it is clear that the first face 210 of the first type polyhedron 202a and the first face 230 and the second face 232 of the second type polyhedron 202b are congruent. This congruence, together with the relationship of the other edges of the two types of tetrahedrons, the order of the first type polyhedrons and the second type polyhedrons in the continuous loop described above, and the arrangement of the hinges, 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 having three orthogonal faces. Such an arrangement having three orthogonal faces is useful for the construction of various parallelepiped configurations (e.g., the inverted parallelepiped configuration of Fig. 1, the cuboid of Fig. 7A, and the hinged parallelepiped of Fig. 7B).

[0053] 4A-4C, we now describe in detail an exemplary hinge arrangement 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 those depicted in FIGS. 3A-3B). between a first edge of a first type tetrahedron and a first edge of an adjacent second type tetrahedron (FIG. 4A shows a bridge strip 204a extending from a first edge 218 of a (first type) polyhedron 202a to a first edge 238 of a (second type) polyhedron 202b); between a first edge of a first type tetrahedron and a fourth edge of an adjacent second type tetrahedron (FIG. 4B shows a bridge strip 204B extending from the first edge 218 of the (first type) polyhedron 202c to the fourth edge 244 of the (second type) 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 hinge types discussed above are arranged around the puzzle 200 in the order discussed 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, the bridge strips are not limited thereto. In some embodiments, the bridge strips are interior type bridge strips that extend through the interior volume of each polyhedron.

[0055] Notwithstanding the representative 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 that is applied to the faces of at least two adjacent polyhedrons such that the hinge extends directly from one of the polyhedrons to the other of the polyhedrons. Although 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 may be applied to two or more polyhedrons. Representative 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 polyhedral module (e.g., a moveable 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 polyhedral 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 internal lumens of the adjacent polyhedrons. Exemplary hinges of this configuration are described in detail in PCT Publication WO2022 / 130285 to Hoenigschmid, which is incorporated herein by reference in its entirety.

[0058] In any embodiment, multiple hinges can 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 Figure 1 and the configurations of Figures 7A-7C. In particular, at least one magnet is disposed on each polyhedron at one location and has a polarity that is magnetically coupled with at least one magnet selected as the opposite polarity disposed on the other polyhedron, such as when puzzle 200 is manipulated into a different configuration.

[0060] In an 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 the first face 210, at least one magnet 250b disposed adjacent the second face 212, at least one magnet 250c disposed adjacent the third face 214, and at least one magnet 250d disposed adjacent the fourth face 216.

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

[0062] In exemplary embodiments, each magnet is embedded in each face, e.g., embedded in a recess (exterior or interior) formed in the face itself. In other embodiments, each magnet can be disposed within the bore of each polyhedron and can be disposed sufficiently close to the associated face such that the magnetic flux of the magnet extends through the face. For example, in some embodiments, each magnet can be held within a groove, slot, and / or track disposed within the bore. In some embodiments, one or more of the magnets can be disposed within brackets (brackets disposed near the vertices of the sides of the polyhedron) such 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 10,569,185 and 10,918,964 to Hoenigschmid, and U.S. Patent Publication No. US2022 / 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 magnet pairs 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 a first type polyhedron and a magnet 252a positioned adjacent to the first face 230 of a second type polyhedron (e.g., a hinged second type polyhedron). A magnet 250a positioned adjacent to a first face 210 of a first type polyhedron and a magnet 252b positioned adjacent to a second face 232 of a second type polyhedron (e.g., a hinged second type polyhedron). A magnet 250b positioned adjacent to the second face 212 of an adjacent first type polyhedron (eg, a hinged first type polyhedron). A magnet 250c positioned adjacent the third face 214 of an adjacent first type polyhedron (eg, a hinged first type 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 of 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), and the polarity alternates 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 of the opposite polarity, 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 manufacturing costs of the puzzle, even at the expense of reduced magnetic stability.

[0066] 6A-6D show diagrams of puzzle 600 in one of the inverted configurations shown in FIG. 1. Puzzle 600 is the same as puzzle 100 of FIG. 1, in that 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 passing completely through it. Magnetically stabilized puzzles with such a geometry were not previously known. Thus, the geometry of puzzle 600, together with the magnets placed in the polyhedrons, impart 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 having the same geometry as puzzle 100 of FIG. 1, in the same hinged arrangement, and including a polyhedron having the same geometry as shown in FIGS. 2 and 3A-3B.

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

[0070] FIG. 7A shows a cubic hexahedron or cubic parallelepiped polyhedron that can be implemented in the puzzle 100. The cubic hexahedron configuration is ideal for packaging and shipping the puzzle 100, given its uniformity and compact size. Interestingly, the puzzle 700 includes polyhedrons with at least two different geometries, but the cubic hexahedron of FIG. 7A can be realized because in the configuration shown in FIG. 7A, only first-kind polyhedrons are presented. That is, in the configuration of FIG. 7A, the outer surface is composed of congruent first-kind polyhedrons 702a, 702c, 702d, 702f, 702g, 702i, 702j, 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 a 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 forth by analogy.

[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. A skilled user will appreciate that the method described below can be modified to achieve congruent inverted configurations of the outermost surfaces that are mutually exclusive.

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

[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 to one another) such that puzzle 800 is oriented in a linear configuration generally represented by longitudinal axis 858. For example, polyhedron 802j (a first type of polyhedron) is positioned adjacent to polyhedron 802k (a second type of polyhedron), polyhedron 802a (a first type of polyhedron) is positioned adjacent to polyhedron 802h (a second type of polyhedron), and so forth.

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

[0080] Returning to Figure 8A, the end polyhedrons are rotated inward until they are hinged to the corresponding penultimate polyhedron. In the illustrated embodiment, polyhedrons 802j and 802k are rotated inward onto polyhedrons 802i and 802l, respectively. Similarly, polyhedrons 802D and 802e are rotated inward onto each other, resulting in the configuration shown in Figure 8B.

[0081] 8B, in this intermediate configuration, the puzzle 800 is generally represented by a vertical axis 858 and a horizontal axis 860 perpendicular thereto. On each side of the vertical axis 858, the puzzle 800 has three representation points (one center point and two outer points) that comprise the vertices of one or more polyhedra. The polyhedra are then manipulated such that on a first side of the vertical axis 858, the center point intersects with an outer point on a first side of the horizontal axis 860. For example, the points of the polyhedra 802b, 802c are brought together in a first "quadrant" of the axes 858, 860. Furthermore, the polyhedra are manipulated such that on a second side (opposite the first side) of the vertical axis 858, the center point intersects with an outer point on a second side (opposite the first side) of the 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 the outermost points are rotated 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 will eventually and naturally rotate polyhedrons 802a, 802h away from each other in opposite directions along lateral axis 860. Thus, puzzle 800 achieves the parallelepiped inverted 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 FIG. 1 and FIG. 6A-6D. As shown, the puzzle 800 has a hole 864 passing through it. The hole 864 is a result of the different geometries between the first type polyhedron and the second type polyhedron. For example, polyhedrons 802a and 802b are connected to each other at hinge 804a and have different geometries. That is, polyhedron 802a is the first type polyhedron shown in FIG. 3A and polyhedron 802b is the second type polyhedron shown in FIG. 3B. The same is true for polyhedrons 802g and 802h. Thus, the different edge lengths between the first type polyhedron and the second type polyhedron form the hole 864.

[0084] The above considered features combine to give the puzzle a number of 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. Hinge connections in successive loops allow 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 obtain many magnetically stable configurations that can provide visual and tactile appeal, 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, stabilizing the puzzle with specific configuration alignments and polarizing magnets in all key configurations gives it a delightful sense of solid quality.

[0087] It should be understood that the above advantages may result from any single feature or from any non-obvious combination of the above 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 a 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 those skilled in the art. The terms used in the description of the present invention herein are for the purpose of describing specific examples only and are not intended to limit the present invention. The term "and / or" used herein includes any and all combinations of the associated listed items.

Claims

1. A dual geometry puzzle, a continuous loop of 12 polyhedrons connected to each other via hinges; eight of the twelve polyhedrons are first type polyhedrons having a first geometric shape and four of the twelve polyhedrons are second type 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 polyhedrons 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. A dual geometry puzzle as described in claim 1, wherein all of the outermost surfaces of the first inverted configuration and all of the outermost surfaces of the second configuration are mutually exclusive.

3. 2. The dual geometry puzzle of claim 1, wherein the twelve polyhedrons are connected via the hinges in a repeating order of one said first type polyhedron, one said second type polyhedron, a second said first type polyhedron, and so on, to form the continuous loop.

4. A dual geometry puzzle as described in claim 1, wherein each of the first type polyhedron and the second type 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 type polyhedron and the second type polyhedron 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 polyhedrons and a first and second face of each of the second kind polyhedrons are congruent.

8. 8. The dual geometry puzzle of claim 7, wherein a fourth face of each of said first kind polyhedrons and a third and fourth face of each of said 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 type polyhedrons 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 type polyhedrons is a tetrahedron having six sides, including two sides having a side length of 1 unit, one side 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 two sides having a side length of √(3) units, which is the square root of 3 units.

12. A dual geometry puzzle as described in claim 3, wherein a first face of each of the first type polyhedrons and a first face and a second face of each of the second type polyhedrons are congruent.

13. A dual geometry puzzle as described in claim 12, wherein each of the first type polyhedrons 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 dual geometry puzzle, a continuous loop of 12 polyhedrons connected to each other via hinges; eight of the twelve polyhedrons are first type polyhedrons having a first geometric shape and four of the twelve polyhedrons are second type 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 first face of each of said first kind polyhedrons and a first face and a second face of each of said second kind polyhedrons are congruent.

15. A dual geometry puzzle as described in claim 14, wherein the fourth face of each of the first type polyhedrons and the third and fourth faces of each of the second type polyhedrons are congruent.

16. A dual geometry puzzle as described in claim 15, wherein the twelve polyhedrons are connected via the hinges in a repeating order of one said first type polyhedron, one said second type polyhedron, and a second said first type polyhedron, thereby forming the continuous loop.

17. A dual geometry puzzle as described in claim 14, wherein the twelve polyhedrons are connected via the hinges in a repeating order of one said first type polyhedron, one said second type polyhedron, and a second said first type polyhedron, thereby forming the continuous loop.

18. A dual geometry puzzle as described in claim 17, wherein each of the first type polyhedron and the second type polyhedron 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.

19. A dual geometry puzzle as described in claim 17, wherein each of the first type polyhedrons 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 type polyhedron and the second type polyhedron 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. A dual geometry puzzle as described in claim 14, wherein each of the first type polyhedrons 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. A dual geometry puzzle as described in claim 21, wherein each of the second type polyhedrons is a tetrahedron having six sides, the six sides including two sides having a side length of 1 unit, one side 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 two sides having a side length of √(3) units, which is the square root of 3 units.

23. The continuous loop of polyhedrons 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 configuration are mutually exclusive.

24. A dual geometry puzzle as described in claim 23, wherein the twelve polyhedrons are connected via the hinges in a repeating order of one said first type polyhedron, one said second type polyhedron, and a second said first type polyhedron, thereby forming the continuous loop.

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

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

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