Collapsible structures may be formed from planar solids. The structures may be comprised of multiple planar objects hingedly connected, where each planar object may include magnetic materials (e.g., magnets, ferromagnetic metals) or electromagnetic materials. Using the magnetic or electromagnetic materials, the connected planar objects may be arranged as a single planar object with multiple layers, or may be arranged as a three-dimensional (3-D) object, where the magnetic or electromagnetic materials may be used to retain the formed 3-D object shape. Application of a current to the electromagnetic materials may cause the collapsible structure to form the 3-D object, and removal of the electric current may cause the collapsible structure to revert to a single planar object. Multiple structures may be combined to form larger structures.

A multiple rhombic dodecahedron puzzle includes a plurality of wooden puzzles arranged in a multiple rhombic dodecahedron. The multiple rhombic dodecahedron is equivalent to a cube formed by a plurality of rhombic dodecahedrons connecting to each other. Each of the wooden puzzles includes two unit elements. The two unit elements are connected to each other and are the same others. Each of the two unit elements has a plurality of surfaces. Each of the surfaces has a diamond shape or a triangular shape. Two of the surfaces which in the triangular shape are connected to each other in order to form a concave shape.

An object is to provide, in place of a cube toy such as Yoshimoto Cube, a wide variety of playing patterns, playing patterns which cannot be predicted in terms of change in forms, a polyhedral toy which can be enjoyed in terms of change in form even when only one polyhedral toy is used, and a polyhedral toy having extensibility for achieving a wide variety of contents of play through combination of two or more polyhedral toys. Therefore, when a polyhedral piece (U1) forming the toy is formed with three quadrangular pyramids (G1 to G3) having, among six triangular faces (T1 to T6) of a cube (R), three faces (R1 to R3) as bottom faces, the polyhedral piece (U1) includes a triangle surface (10) formed of six triangular faces (T1 to T6) other than respective side faces of the quadrangular pyramids (G1 to G3) placed on one another. When polyhedral pieces (U1 to U8) each having the configuration described above form a toy (1) unfolded into a cuboid shape of two rows and four columns as illustrated in FIG. 1, in plan view on a top face of the toy (1), in each of the first row and the second row, the triangle surface (10), the third face (R3), the third face (R3), and the triangle surface (10) are arranged in the stated order.

An object is to provide, in place of a cube toy such as Yoshimoto Cube, a wide variety of playing patterns, playing patterns which cannot be predicted in terms of change in forms, a polyhedral toy which can be enjoyed in terms of change in form even when only one polyhedral toy is used, and a polyhedral toy having extensibility for achieving a wide variety of contents of play through combination of two or more polyhedral toys. Therefore, when a polyhedral piece (U1) forming the toy is formed with three quadrangular pyramids (G1 to G3) having, among six triangular faces (T1 to T6) of a cube (R), three faces (R1 to R3) as bottom faces, the polyhedral piece (U1) includes a triangle surface (10) formed of six triangular faces (T1 to T6) other than respective side faces of the quadrangular pyramids (G1 to G3) placed on one another. When polyhedral pieces (U1 to U8) each having the configuration described above form a toy (1) unfolded into a cuboid shape of two rows and four columns as illustrated in FIG. 1, in plan view on a top face of the toy (1), in each of the first row and the second row, the triangle surface (10), the third face (R3), the third face (R3), and the triangle surface (10) are arranged in the stated order.

A panel and a system for use in building a lightweight structure are provided. The panel, made of a film or a sheet capable of being curved or bent with fingers, includes a body in a geometric shape circumscribed by straight or curved edges, and at least one joint formation along the edge for panel connection. The joint formation has tabs separated by at least one gap. Each tab expands bilaterally and proximally from the body at its base, and each gap is positioned along the edge so as to accept the base of the tab. The joint formations along the edges of varied curvatures are alignedly, hingedly, and detachably interlocked with each other by twisting the panels with fingers to individually hook the tab at the gap. The panels are assembled into geometric structures having flat or curved faces.

A multiple rhombic dodecahedron puzzle includes a plurality of wooden puzzles arranged in a multiple rhombic dodecahedron. The multiple rhombic dodecahedron is equivalent to a cube formed by a plurality of rhombic dodecahedrons connecting to each other. Each of the wooden puzzles includes two unit elements. The two unit elements are connected to each other and are the same others. Each of the two unit elements has a plurality of surfaces. Each of the surfaces has a diamond shape or a triangular shape. Two of the surfaces which in the triangular shape are connected to each other in order to form a concave shape.

A multiple rhombic dodecahedron puzzle includes a plurality of wooden puzzles arranged in a multiple rhombic dodecahedron. The multiple rhombic dodecahedron is equivalent to a cube formed by a plurality of rhombic dodecahedrons connecting to each other. Each of the wooden puzzles includes two unit elements. The two unit elements are connected to each other and are the same others. Each of the two unit elements has a plurality of surfaces. Each of the surfaces has a diamond shape or a triangular shape. Two of the surfaces which in the triangular shape are connected to each other in order to form a concave shape, and the surfaces are surrounded to form a closed space.

A panel and a system for use in building a lightweight structure are provided. The panel, made of a film or a sheet capable of being curved or bent with fingers, includes a body in a geometric shape circumscribed by straight or curved edges, and at least one joint formation along the edge for panel connection. The joint formation has tabs separated by at least one gap. Each tab expands bilaterally and proximally from the body at its base, and each gap is positioned along the edge so as to accept the base of the tab. The joint formations along the edges of varied curvatures are alignedly, hingedly, and detachably interlocked with each other by twisting the panels with fingers to individually hook the tab at the gap. The panels are assembled into geometric structures having flat or curved faces.

A multiple rhombic dodecahedron puzzle includes a plurality of wooden puzzles arranged in a multiple rhombic dodecahedron. The multiple rhombic dodecahedron is equivalent to a cube formed by a plurality of rhombic dodecahedrons connecting to each other. Each of the wooden puzzles includes two unit elements. The two unit elements are connected to each other and are the same others. Each of the two unit elements has a plurality of surfaces. Each of the surfaces has a diamond shape or a triangular shape. Two of the surfaces which in the triangular shape are connected to each other in order to form a concave shape, and the surfaces are surrounded to form a closed space.

A system for generating a three-dimensional puzzle comprises a processor and a memory. The processor is configured to generate a three dimensional mesh representation. The processor is further configured to convert polygons comprising the three-dimensional mesh representation to one or more puzzle piece representations. The processor is further configured to add attachment points and receiving points to the one or more puzzle piece representations. The processor is further configured to provide the one of more puzzle piece representations with attachment points and receiving points. The memory is coupled to the processor and configured to provide the processor with instructions.