Three-dimensional construction blocks with configuration-invariant attachment

Abstract

A construction block system includes a shell, where the shell forms a cell of the system. The system also includes one or more magnets embedded in each of the exterior sides of the shell, where the one or more magnets are mounted such that magnets along opposing faces of aligned cells have opposite poles.

Description

THREE-DIMENSIONAL CONSTRUCTION BLOCKS WITH CONFIGURATIONINVARIANT ATTACHMENTCROSS-REFERENCE TO RELATED APPLICATION

[0001] The present application claims the priority benefit of U.S. Provisional Patent App. No. 63 / 618,628 filed on January 8, 2024, the entire disclosure of which is incorporated by reference herein.BACKGROUND

[0002] Space-filling building blocks of diverse shape and size permeate nature at all levels of organization. These space-filling blocks have also proven useful in artificial systems such as molecular containers, clay bricks, toys, etc. However, despite the wide variety of space-filling polyhedra know n to mathematics, in many fields only the cube has been explored for practical applications. This is due in part to the simplistic shape of the cube and the ease in manufacturing of cubic shapes.SUMMARY

[0003] An illustrative construction block system includes a shell, where the shell forms a cell of the system. The system also includes one or more magnets embedded in each of the exterior sides of the shell, where the one or more magnets are mounted such that magnets along opposing faces of aligned cells have opposite poles.

[0004] In one embodiment, the shell is in the shape of a rhombic dodecahedron. In another embodiment, the shell includes a first portion and a second portion that are mounted to one another to form the rhombic dodecahedron. In another embodiment, the magnets comprise axially -poled neodymium magnets. In one embodiment, the cell includes twelve faces, and each face of the cell includes at least 4 magnets.

[0005] In another embodiment, the one or more magnets comprises a single multi-pole magnet. In one embodiment, the single multi-pole magnet has eight poles. In another embodiment, the single multi-pole magnet includes an upper layer and a lower layer. In such an embodiment, the upper layer includes first magnetic portions that alternative between north pole areas and south pole areas and the lower layer includes second magnetic portions that alternative between north pole areas and south pole areas. In another embodiment, the first magnetic portions of the upper layer and second magnetic portions of the lower layer arestacked such that opposing poles are stacked adjacent to one another. In another embodiment, the one or more magnets includes a dipole magnet positioned about each symmetry’ line on each exterior side of the block. In another embodiment, each symmetry line originates from a comer formed by the exterior side of the block.

[0006] An illustrative method of forming a construction block system includes forming a shell that is a cell of the system. The method also includes embedding one or more magnets in each of the exterior sides of the shell, where the one or more magnets are mounted such that magnets along opposing faces of aligned cells have opposite poles.

[0007] In one embodiment, forming the shell comprises forming the cell in the shape of a rhombic dodecahedron. In another embodiment, the one or more magnets comprise axially- poled neodymium magnets. In another embodiment, the cell includes twelve faces, and wherein each face of the cell includes at least 4 magnets. In another embodiment, embedding the one or more magnets comprises embedding a single multi-pole magnet in each of the exterior sides of the shell. In another embodiment, the single multi-pole magnet has eight poles. In another embodiment, the single multi-pole magnet includes an upper layer and a lower layer, where the upper layer includes first magnetic portions that alternative between north pole areas and south pole areas, and where the lower layer includes second magnetic portions that alternative between north pole areas and south pole areas

[0008] Other principal features and advantages of the invention will become apparent to those skilled in the art upon review of the following drawings, the detailed description, and the appended claims.BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Illustrative embodiments of the invention will hereafter be described with reference to the accompanying drawings, wherein like numerals denote like elements.

[0010] Fig. 1 A depicts a pole-locking configuration that occurs in traditional construction block systems in accordance with an illustrative embodiment.

[0011] Fig. IB depicts top, front, and isometric views of an 8 pole magnet in accordance with an illustrative embodiment.

[0012] Fig 2 is a rhombus face with N-fold symmetry: n = 2, degrees of rotation between symmetric orientations: 9 =180°, and number of connectors: x = 4 in accordance with an illustrative embodiment.

[0013] Fig 3 is a rectangle face with N-fold symmetry: n = 2. degrees of rotation between symmetric orientations: 9 = 180°, and number of connectors: x = 4 in accordance with an illustrative embodiment.

[0014] Fig 4 is an equilateral triangle face with N-fold symmetry: n = 3, degrees of rotation between symmetric orientations: 9 = 120°, and number of connectors: x = 6 in accordance with an illustrative embodiment.

[0015] Fig. 5 is a square face with N-fold symmetry: n = 4, degrees of rotation between symmetric orientations: 9 =90°. and number of connectors: x = 8 in accordance with an illustrative embodiment.

[0016] Fig 6 is a regular pentagon face with N-fold symmetry: n = 5, degrees of rotation between symmetric orientations: 9 =72°, and number of connectors: x = 10 in accordance with an illustrative embodiment.

[0017] Fig. 7 is a regular hexagon face with N-fold symmetry': n = 6, degrees of rotation between symmetric orientations: 9 = 60°, and number of connectors: x = 12 in accordance with an illustrative embodiment.

[0018] Fig. 8 is a regular heptagon face with N-fold symmetry: n = 7, degrees of rotation between symmetric orientations: 9 = 51.43°, and number of connectors: x = 14 in accordance with an illustrative embodiment.

[0019] Fig. 9 is a regular octagon face with N-fold symmetry: n = 8, degrees of rotation between symmetric orientations: 9 = 45°, and number of connectors: x = 16 in accordance with an illustrative embodiment.

[0020] Fig. 10 is a regular nonagon face with N-fold symmetry: n = 9, degrees of rotation between symmetric orientations: 9 = 40°, and number of connectors: x = 18 in accordance with an illustrative embodiment.

[0021] Fig. 1 1 is a regular decagon face with N-fold symmetry: n = 10. degrees of rotation betw een symmetric orientations: 9 = 36°, and number of connectors: x = 20 in accordance with an illustrative embodiment.

[0022] Fig. 12 is a regular hendecagon face with N-fold symmetry': n =11, degrees of rotation between symmetric orientations: 6 = 32.73°, and number of connectors: x = 22 in accordance with an illustrative embodiment.

[0023] Fig. 13 is a regular dodecagon face with N-fold symmetry: n =12. degrees of rotation between symmetric orientations: 6 = 30°, and number of connectors: x = 24 in accordance with an illustrative embodiment.

[0024] Fig. 14A shows a cube with vertices: 8, edges: 12, and faces: 6 (6 squares) in accordance with an illustrative embodiment.

[0025] Fig. 14B depicts a plurality' of cubes mounted to one another in accordance with an illustrative embodiment.

[0026] Fig. 15A is a regular tetrahedron with vertices: 4, edges: 6, and faces: 4 (4 equilateral triangles) in accordance with an illustrative embodiment.

[0027] Fig. 15B depicts a plurality of regular tetrahedrons mounted to one another in accordance with an illustrative embodiment.

[0028] Fig. 16A is a regular octahedron with vertices: 6, edges: 12, and faces: 8 (8 equilateral triangles) in accordance with an illustrative embodiment.

[0029] Fig. 16B depicts a plurality of regular octahedrons mounted to one another in accordance with an illustrative embodiment.

[0030] Fig. 17A is a regular dodecahedron with vertices: 20, edges: 30. and faces: 12 (12 regular pentagons) in accordance with an illustrative embodiment.

[0031] Fig. 17B depicts a plurality of regular dodecahedrons mounted to one another in accordance with an illustrative embodiment.

[0032] Fig. 18A is a regular icosahedron with vertices: 12, edges: 30, and faces: 20 (20 equilateral triangles) in accordance with an illustrative embodiment.

[0033] Fig. 18B depicts a plurality7of regular icosahedrons mounted to one another in accordance with an illustrative embodiment.

[0034] Fig. 19A is an acute golden rhombohedron with vertices: 8, edges: 12, and faces: 6 (6 rhombi) in accordance with an illustrative embodiment.

[0035] Fig. 19B depicts a plurality of acute golden rhombohedrons mounted to one another in accordance with an illustrative embodiment.

[0036] Fig. 20A is an elongated dodecahedron with vertices: 18, edges: 28. and faces: 12 (8 rhombi, 4 hexagons) in accordance with an illustrative embodiment.

[0037] Fig. 20B depicts a plurality of elongated dodecahedrons mounted to one another in accordance with an illustrative embodiment.

[0038] Fig. 21A is a gyrobifastigium with vertices: 8. edges: 14, and faces: 8 (4 squares, 4 equilateral triangles) in accordance with an illustrative embodiment.

[0039] Fig. 2 IB depicts a plurality of gyrobifastigiums mounted to one another in accordance with an illustrative embodiment.

[0040] Fig. 22A is a rhombic dodecahedron with vertices: 14, edges: 24, and faces: 12 (12 rhombi) in accordance with an illustrative embodiment.

[0041] Fig. 22B depicts a plurality of rhombic dodecahedrons mounted to one another in accordance with an illustrative embodiment.

[0042] Fig. 23A is a truncated octahedron with vertices: 24, edges: 36, and faces: 14 (6 rhombi, 8 hexagons) in accordance with an illustrative embodiment.

[0043] Fig. 23B depicts a plurality of truncated octahedrons mounted to one another in accordance with an illustrative embodiment.

[0044] Fig. 24A is a tri diminished icosahedron with vertices: 9, edges: 15, and faces: 8 (5 equilateral triangles, 3 pentagons) in accordance with an illustrative embodiment.

[0045] Fig. 24B depicts a plurality of tridiminished icosahedrons mounted to one another in accordance with an illustrative embodiment.

[0046] Fig. 25A is a bilunabirotunda with vertices: 14, edges: 26, and faces: 14 (8 equilateral triangles, 2 squares, 4 pentagons) in accordance with an illustrative embodiment.

[0047] Fig. 25B depicts a plurality of bilunabirotundas mounted to one another in accordance with an illustrative embodiment.

[0048] Fig. 26A is a disphenocingulum with vertices: 16, edges: 38, and faces: 24 (20 equilateral triangles, 4 squares) in accordance with an illustrative embodiment.

[0049] Fig. 26B depicts a plurality of disphenocingulums mounted to one another in accordance with an illustrative embodiment.

[0050] Fig. 27A is a sphenocorona with vertices: 10, edges: 22, and faces: 14 (12 equilateral triangles, 2 squares) in accordance with an illustrative embodiment.

[0051] Fig. 27B depicts a plurality of sphenocoronas mounted to one another in accordance with an illustrative embodiment.

[0052] Fig. 28A is a square gyrobicupola in accordance with an illustrative embodiment.

[0053] Fig. 28B depicts a plurality of gyrobicupolas mounted to one another in accordance with an illustrative embodiment.

[0054] Fig. 29A is an equilateral triangular prism with vertices: 6, edges: 9, and faces: 5 (2 equilateral triangles, 3 squares) in accordance with an illustrative embodiment.

[0055] Fig. 29B depicts a plurality of equilateral triangular prisms mounted to one another in accordance with an illustrative embodiment.

[0056] Fig. 30A is an equilateral pentagonal prism with vertices: 10, edges: 15, and faces:7 (2 pentagons, 5 squares) in accordance with an illustrative embodiment.

[0057] Fig. 30B depicts a plurality of equilateral pentagonal prisms mounted to one another in accordance with an illustrative embodiment.

[0058] Fig. 31A is an equilateral hexagonal prism with vertices: 12, edges: 18, and faces:8 (2 hexagons, 6 squares) in accordance with an illustrative embodiment.

[0059] Fig. 3 IB depicts a plurality' of equilateral hexagonal prisms mounted to one another in accordance with an illustrative embodiment.

[0060] Fig. 32A is an equilateral heptagonal prism with vertices: 14, edges: 21, and faces:9 (2 heptagons, 7 squares) in accordance with an illustrative embodiment.

[0061] Fig. 32B depicts a plurality of equilateral heptagonal prisms mounted to one another in accordance with an illustrative embodiment.

[0062] Fig. 33A is an equilateral octagonal prism with vertices: 16, edges: 24, and faces:10 (2 octagons, 8 squares) in accordance with an illustrative embodiment.

[0063] Fig. 33B depicts a plurality of equilateral octagonal prisms mounted to one another in accordance with an illustrative embodiment.

[0064] Fig. 34 depicts a rhombic dodecahedron prototype block (left) and a plurality of rhombic dodecahedron blocks connected to one another (right) in accordance with an illustrative embodiment.

[0065] Fig. 35 depicts a gyrobifastigium prototype block (left) and a plurality of gyrobi fasti gium blocks (right) connected to one another in accordance with an illustrative embodiment.

[0066] Fig. 36A depicts electronics in an interior of a rhombic dodecahedral shape in accordance with an illustrative embodiment.

[0067] Fig. 36B depicts a plurality of rhombic dodecahedral cells connected to form an (actuated or non-actuated) superstructure in accordance with an illustrative embodiment.

[0068] Fig. 37A depicts 90° block motion in accordance with an illustrative embodiment.

[0069] Fig. 37B depicts 180° block motion in accordance with an illustrative embodiment.

[0070] Fig. 37C is a two-dimensional (2D) projection of rhombic dodecahedron rotation (hexagon) in accordance with an illustrative embodiment.

[0071] Fig. 38 is an exploded view of a rhombic dodecahedral robotic cell in accordance with an illustrative embodiment.

[0072] Fig. 39A depicts symmetry lines about which magnets are mounted on the rhombic dodecahedron robotic cells in accordance with an illustrative embodiment. As shown, the magnet arrangement takes advantage of the symmetry lines that are positioned along the long axis of the rhombic faces of the cells.

[0073] Fig. 39B depicts a jig that was designed and 3D printed to simplify cell assembly in accordance with an illustrative embodiment.

[0074] Fig. 40A depicts a single rhombic dodecahedron robotic cell in accordance with an illustrative embodiment.

[0075] Fig. 40B depicts a structure formed by a pair of rhombic dodecahedron robotic cells in accordance with an illustrative embodiment.

[0076] Fig. 40C depicts a structure formed by three rhombic dodecahedron robotic cells in accordance with an illustrative embodiment.

[0077] Fig. 40D depicts a structure formed by four rhombic dodecahedron robotic cells in accordance with an illustrative embodiment.

[0078] Fig. 40E depicts a structure formed by twelve rhombic dodecahedron robotic cells in accordance with an illustrative embodiment.

[0079] Fig. 40F depicts a structure formed by twenty rhombic dodecahedron robotic cells in accordance with an illustrative embodiment.

[0080] Fig. 40G depicts a structure formed by twenty-two rhombic dodecahedron robotic cells in accordance with an illustrative embodiment.

[0081] Fig. 40H depicts a structure formed by thirty rhombic dodecahedron robotic cells in accordance with an illustrative embodiment.

[0082] Fig. 401 depicts a structure formed by thirty -nine dodecahedron robotic cells in accordance with an illustrative embodiment.

[0083] Fig. 40J depicts a structure formed forty-two rhombic dodecahedron robotic cells in accordance with an illustrative embodiment.

[0084] Fig. 40K depicts a structure formed by forty -six rhombic dodecahedron robotic cells in accordance with an illustrative embodiment.

[0085] Fig. 40L depicts a structure formed by forty-eight rhombic dodecahedron robotic cells in accordance with an illustrative embodiment.

[0086] Fig. 41 A depicts a locomotion pattern for a robotic system with three rhombic dodecahedron robotic cells in accordance with an illustrative embodiment.

[0087] Fig. 41B depicts a locomotion pattern for a robotic system with four rhombic dodecahedron robotic cells in accordance with an illustrative embodiment.

[0088] Fig. 41C depicts a locomotion pattern for a robotic system with seven rhombic dodecahedron robotic cells in accordance with an illustrative embodiment.

[0089] Fig. 41D depicts a locomotion pattern for a robotic system with ten rhombic dodecahedron robotic cells in accordance with an illustrative embodiment.

[0090] Fig. 42 depicts a table that summarizes morphological and behavioral characterization of the designs from Fig. 41 in accordance with an illustrative embodiment.

[0091] Fig. 43 depicts a computing device in direct or indirect communication with a network in accordance with an illustrative embodiment.DETAILED DESCRIPTION

[0092] Described herein is a novel mechanism for orientation-invariant and configuration-invariant attachment of building blocks, or groups of blocks, that guarantees full attachment. Existing construction toys, such as Magna-Cubix, etc. include building blocks capable of attaching in a three-dimensional (3D) space. However, in traditional systems, the attachment mechanism relies on freely -rotating comer-embedded magnets, which often leads to pole-locking, where an open face of a block cannot accept a new connection because the magnets are preoccupied supporting connections on other faces. It is easy to demonstrate simple configurations of these existing blocks that completely inhibit connection. For example, Fig. 1 A depicts a pole-locking configuration that occurs in traditional construction block systems in accordance with an illustrative embodiment. As shown, the blocks are three-sided and each of the three comers includes a rotating magnet that has a north pole and a south pole. Fig. 1 A depicts two of the blocks connected to one another such that the magnets are attracted to one another (i.e., the magnets rotate such that opposite poles (N-S or S-N) are adjacent to one another. Fig. 1 A also depicts three of the blocks connected to one another such that the magnets are attracted to one another. The far right image of Fig. 1 A shows a pole-locking scenario in which two groups of the blocks cannot connect to one another because each group’s magnets are locked in place, and are thus unable to rotate to support the new connection.

[0093] The pole-locking problem limits the size and shape of the aggregate structures that can be constructed with existing 3D building blocks. Moreover, existing systems do not scale to block shapes with more than a small number of faces. Described herein is a novel attachment method that allows groups of building blocks of arbitrary 3D shape to fully attach, in any orientation and in any configuration. In one illustrative embodiment, this is accomplished by positioning a pair of male / female connectors about each line of rotational symmetry along each face of the building block. This method can be applied to any block with faces that have radial symmetry'. Examples are described herein for radially symmetrical faces and example blocks that contain them. The proposed method can also be extended to other blocks with other radially symmetrical faces. Additionally, although magnets are described in the primary embodiment, the connectors used to connect blocks can extend toarbitrary male / female connectors, such as hook / latch mechanical connections, hook / loop Velcro, etc.

[0094] In another embodiment, instead of mounting a dipole magnet about each line of rotation symmetry of the block, a single multi-pole magnet can be used on each face of the 3D block. Fig. IB depicts top, front, and isometric views of an 8 pole magnet in accordance with an illustrative embodiment. As shown in the isometric view, the 8 pole magnet has an upper layer and a lower layer. The upper layer includes 4 portions that alternate between north pole magnet areas and south pole magnet areas. The lower layer similarly includes 4 portions that alternative between north pole areas and south pole magnet areas. The upper and lower layers of magnets are stacked such that opposing poles are stacked adjacent to one another. As shown, a north pole on the low er layer has a south pole magnet area stacked on top thereof, and vice versa. One or more of these multi-pole magnets can be mounted on each face of a block to allow any configuration of the blocks to connect, and to eliminate the polelocking that occurs in traditional systems. In alternative embodiments, the multi-pole magnet can have a different number of poles such as 4, 16, 32, etc. In another embodiment, the multipole magnet can be a spherical magnet that includes a plurality of magnetic poles.

[0095] There are many w ays to arrange the magnets in the shell to ensure a stable connection. For example, magnets can be placed in the comers of each face in one embodiment. However, this would not always allow for two geometrically aligned cells to connect magnetically. While anew cell could always be rotated to connect to the end of a ID chain, in 2D and 3D structures a valid rotation will not alw ays be possible, rendering connections unstable (one or more pairs of magnets are repulsive) or impossible (no pairs of magnets are attractive). To ensure genderless docking, pairs of magnets along the two opposing faces of two aligned cells must preserve their unlike poles under 180° rotations. The magnet configurations depicted herein satisfy this constraint. With this magnet configuration, cells can connect within the entire face-centered cubic lattice-configuration that is characteristic of rhombic dodecahedra and the other shapes discussed herein.

[0096] Despite the simplicity that passive magnetic docking enables, complications can still arise. For example, due to the smooth surface finish of commercially available magnets, glue could does not properly adhere to their surface. As a result, embedded magnets can be prone to falling out. However, it w as found that this problem can be ameliorated by sanding down (or otherwise roughing up) the surface finish of the magnets to increase their roughnessand surface friction prior to mounting by creating grooves, etc. in the magnet. This greatly reduced the number of magnets that dislodged from the face during reconfiguration. In one embodiment, the magnets can be rectangular and can have a dimension of 2.5 millimeters (mm) by 3.5 mm. Alternatively, a different shape and / or dimensions may be used for the magnets. In another illustrative embodiment, the magnets used herein can be axially-poled neodymium magnets.

[0097] Another challenge was that embedding magnets manually, one by one, is a time consuming and labor intensive task that is time consuming. This challenge was addressed by designing a jig to hold the magnets and guide them into place, as shown in Fig. 39B. As discussed in more detail below, the jig includes three main components, a base that holds and supplies the magnets, a slider that has identical magnet configurations as the cells, and a removable slider top. The slider is moved through the slot in the base allowing the magnets to reload themselves into the desired location. The slider top can then be removed and the entire face of a cell can be mounted simultaneously. With these refinements, one cell can be embedded with magnets in a significantly shorter amount of time, and the overall assembly time is now primarily limited by the curing time of the glue used for mounting.

[0098] Many unit shapes have been explored in block building sy stems, such as triangles, hexagons, spheres, cubes, cuboids, cylinders, semi-cylinders, and cylindroids. However, only- two of these previously used shapes were built to attach in 3D space (spheres and cubes), and only one (cubes) is capable of filling such a 3D space. The cube is a parallelohedron, which is a congruent polyhedron that can be translated to completely fill space, without rotations. In other words, space can be partitioned into a regular lattice by cubes. In addition to the cube, which has square faces, there are just four other parallelohedra: the rhombic dodecahedron (rhombic faces), the hexagonal prism (hexagonal and cubic faces), the elongated dodecahedron (rhombic and octagonal faces), and the truncated octahedron (cubic, rhombic, and hexagonal faces). The cube and the rhombic dodecahedron are the simplest parallelohedra. Their isometric faces (all squares or all rhombi) allow two cells to connect on all sides, which simplifies the assembly and reconfiguration of multicellular bodies.

[0099] There is an infinitude of other polyhedra that, alone or in combination with additional polyhedra, via translations, rotations or reflections, along periodic or aperiodic tilings, can fill space without any gaps. Out of all of these possible shapes, the cube is most often considered in block building applications. However, as discussed herein, cubes andcuboids are limited in their application and do not provide the flexibility' and efficiency that can be obtained by using rhombic dodecahedra and other shapes as a non-cubic space-filling shape.

[0100] The rhombic dodecahedron geometry (along with the other shapes described herein) offers an appealing alternative to cubes as it greatly simplifies rotational motion of one cell about the edge of another, and increases the number of neighbors each cell can hold on to. To better understand the challenges and opportunities of these and other space-filling machines, the inventors manufactured rhombic dodecahedral blocks and used them to build various superstructures. Included below is a discussion of various shapes that can be used to implement the proposed block building system. In alternative embodiments, other shapes and / or magnet configurations can be used.

[0101] The following figures include depictions of various ty pes of block faces that can be used to form blocks of the proposed system. The descriptions of the various blocks include face type, N-fold symmetry (see dashed lines), the degrees of rotation between symmetric orientations (9), and an example number of connectors used. In an illustrative embodiment, each face of a given block can have the same face type. N-fold symmetry', degrees of rotation, and number of connectors. Also, in alternative embodiments, any of the specific values used for any of the blocks can be changed to form new types of faces and / or blocks.

[0102] Fig 2 is a rhombus face with N-fold symmetry: n = 2, degrees of rotation between symmetric orientations: 0 =180°, and number of connectors: x = 4 in accordance with an illustrative embodiment. Fig 3 is a rectangle face with N-fold symmetry: n = 2, degrees of rotation between symmetric orientations: 0 = 180°, and number of connectors: x = 4 in accordance with an illustrative embodiment. Fig 4 is an equilateral triangle face with N-fold symmetry: n = 3. degrees of rotation between symmetric orientations: 0 = 120°, and number of connectors: x = 6 in accordance with an illustrative embodiment. Fig. 5 is a square face with N-fold symmetry: n = 4, degrees of rotation between symmetric orientations: 0 =90°, and number of connectors: x = 8 in accordance with an illustrative embodiment. Fig 6 is a regular pentagon face with N-fold symmetry: n = 5. degrees of rotation between symmetric orientations: 0 =72°, and number of connectors: x = 10 in accordance with an illustrative embodiment. Fig. 7 is a regular hexagon face with N-fold symmetry: n = 6, degrees of rotation between symmetric orientations: 0 = 60°. and number of connectors: x = 12 in accordance with an illustrative embodiment.

[0103] Fig. 8 is a regular heptagon face with N-fold symmetry': n = 7, degrees of rotation between symmetric orientations: 6 = 51.43°, and number of connectors: x = 14 in accordance with an illustrative embodiment. Fig. 9 is a regular octagon face with N-fold symmetry’: n = 8, degrees of rotation between symmetric orientations: 9 = 45°, and number of connectors: x = 16 in accordance with an illustrative embodiment. Fig. 10 is a regular nonagon face with N- fold symmetry: n = 9, degrees of rotation between symmetric orientations: 0 = 40°, and number of connectors: x = 18 in accordance with an illustrative embodiment. Fig. 11 is a regular decagon face with N-fold symmetry’: n = 10, degrees of rotation between symmetric orientations: 0 = 36°, and number of connectors: x = 20 in accordance with an illustrative embodiment. Fig. 12 is a regular hendecagon face with N-fold symmetry: n =11, degrees of rotation between symmetric orientations: 0 = 32.73°, and number of connectors: x = 22 in accordance with an illustrative embodiment. Fig. 13 is a regular dodecagon face with N-fold symmetry': n =12, degrees of rotation between symmetric orientations: 0 = 30°, and number of connectors: x = 24 in accordance with an illustrative embodiment.

[0104] The following figures depict various types of three-dimensional blocks that can be used in the proposed system, along with a series of such blocks connected to one another. Fig. 14A shows a cube with vertices: 8, edges: 12, and faces: 6 (6 squares) in accordance with an illustrative embodiment. Fig. 14B depicts a plurality of cubes mounted to one another in accordance with an illustrative embodiment. As shown, a pair of opposing poles (e.g., a single dipole magnet) is positioned about each symmetry line in each comer of the block. As shown, the symmetry’ lines extend from comers of the block.

[0105] Fig. 15A is a regular tetrahedron with vertices: 4, edges: 6, and faces: 4 (4 equilateral triangles) in accordance with an illustrative embodiment. Fig. 15B depicts a plurality’ of regular tetrahedrons mounted to one another in accordance with an illustrative embodiment. Fig. 16A is a regular octahedron with vertices: 6, edges: 12, and faces: 8 (8 equilateral triangles) in accordance with an illustrative embodiment. Fig. 16B depicts a plurality of regular octahedrons mounted to one another in accordance with an illustrative embodiment. Fig. 17A is a regular dodecahedron with vertices: 20, edges: 30, and faces: 12 (12 regular pentagons) in accordance with an illustrative embodiment. Fig. 17B depicts a plurality of regular dodecahedrons mounted to one another in accordance with an illustrative embodiment.

[0106] Fig. 18A is a regular icosahedron with vertices: 12, edges: 30, and faces: 20 (20 equilateral triangles) in accordance with an illustrative embodiment. Fig. 18B depicts a plurality of regular icosahedrons mounted to one another in accordance with an illustrative embodiment. Fig. 19A is an acute golden rhombohedron with vertices: 8, edges: 12, and faces: 6 (6 rhombi) in accordance with an illustrative embodiment. Fig. 19B depicts a plurality of acute golden rhombohedrons mounted to one another in accordance with an illustrative embodiment. Fig. 20A is an elongated dodecahedron with vertices: 18, edges: 28, and faces: 12 (8 rhombi, 4 hexagons) in accordance with an illustrative embodiment. Fig. 20B depicts a plurality of elongated dodecahedrons mounted to one another in accordance with an illustrative embodiment. Fig. 21 A is a gyrobifastigium with vertices: 8, edges: 14, and faces: 8 (4 squares, 4 equilateral triangles) in accordance with an illustrative embodiment. Fig. 21B depicts a plurality of gyrobifastigiums mounted to one another in accordance with an illustrative embodiment. Fig. 22A is a rhombic dodecahedron with vertices: 14, edges: 24, and faces: 12 (12 rhombi) in accordance with an illustrative embodiment. Fig. 22B depicts a plurality of rhombic dodecahedrons mounted to one another in accordance with an illustrative embodiment. Fig. 23A is a truncated octahedron with vertices: 24, edges: 36, and faces: 14 (6 rhombi, 8 hexagons) in accordance with an illustrative embodiment. Fig. 23B depicts a plurality of truncated octahedrons mounted to one another in accordance with an illustrative embodiment.

[0107] Fig. 24A is a tri diminished icosahedron with vertices: 9, edges: 15, and faces: 8 (5 equilateral triangles, 3 pentagons) in accordance with an illustrative embodiment. Fig. 24B depicts a plurality of tri diminished icosahedrons mounted to one another in accordance with an illustrative embodiment. Fig. 25A is a bilunabirotunda with vertices: 14, edges: 26, and faces: 14 (8 equilateral triangles, 2 squares, 4 pentagons) in accordance with an illustrative embodiment. Fig. 25B depicts a plurality of bilunabirotundas mounted to one another in accordance with an illustrative embodiment. Fig. 26A is a disphenocingulum with vertices: 16, edges: 38, and faces: 24 (20 equilateral triangles, 4 squares) in accordance with an illustrative embodiment. Fig. 26B depicts a plurality of disphenocingulums mounted to one another in accordance with an illustrative embodiment. Fig. 27A is a sphenocorona with vertices: 10, edges: 22. and faces: 14 (12 equilateral triangles, 2 squares) in accordance with an illustrative embodiment. Fig. 27B depicts a plurality of sphenocoronas mounted to one another in accordance with an illustrative embodiment.

[0108] Fig. 28A is a square gyrobicupola in accordance with an illustrative embodiment. Fig. 28B depicts a plurality of gyrobicupolas mounted to one another in accordance with an illustrative embodiment. Fig. 29A is an equilateral triangular prism with vertices: 6, edges: 9, and faces: 5 (2 equilateral triangles, 3 squares) in accordance with an illustrative embodiment. Fig. 29B depicts a plurality' of equilateral triangular prisms mounted to one another in accordance with an illustrative embodiment. Fig. 30A is an equilateral pentagonal prism with vertices: 10, edges: 15. and faces: 7 (2 pentagons, 5 squares) in accordance with an illustrative embodiment. Fig. 30B depicts a plurality of equilateral pentagonal prisms mounted to one another in accordance with an illustrative embodiment. Fig. 31A is an equilateral hexagonal prism with vertices: 12, edges: 18, and faces: 8 (2 hexagons, 6 squares) in accordance with an illustrative embodiment. Fig. 3 IB depicts a plurality of equilateral hexagonal prisms mounted to one another in accordance with an illustrative embodiment. Fig. 32A is an equilateral heptagonal prism with vertices: 14, edges: 21, and faces: 9 (2 heptagons, 7 squares) in accordance with an illustrative embodiment. Fig. 32B depicts a plurality of equilateral heptagonal prisms mounted to one another in accordance with an illustrative embodiment. Fig. 33A is an equilateral octagonal prism with vertices: 16, edges: 24. and faces: 10 (2 octagons, 8 squares) in accordance with an illustrative embodiment. Fig. 33B depicts a plurality of equilateral octagonal prisms mounted to one another in accordance with an illustrative embodiment.

[0109] Fig. 34 depicts a rhombic dodecahedron prototype block (left) and a plurality of rhombic dodecahedron blocks connected to one another (right) in accordance with an illustrative embodiment. Fig. 35 depicts a gyrobifastigium prototype block (left) and a plurality of gyrobifastigium blocks (right) connected to one another in accordance with an illustrative embodiment.

[0110] In one embodiment, the blocks can be actuated such that they are robotic in nature. Fig. 36A depicts electronics in an interior of a rhombic dodecahedral shape in accordance with an illustrative embodiment. The electronics are described in more detail with reference to Fig. 38. Similar to crystals and other natural structures, modular robots can grow to form multicellular bodies by ceaselessly combining and separating unit cells. Such robots — if space-filling — can be used to form gapless containers, pipes, mirrors, shields, submersibles, spaceships, extraterrestrial habitats, etc. on the fly. Also, by virtue of broader surface contacts between neighbors, space-filling robots are able to build much more stable and energetically favorable superstructures than non-space-filling robots. Fig. 36B depicts aplurality of rhombic dodecahedral cells connected to form an (actuated or non-actuated) superstructure in accordance with an illustrative embodiment.

[0111] Rhombic dodecahedra have an advantage kinematically over cubes. Fig. 37 depicts various types of rolling motions for blocks. Specifically, Fig. 37A depicts 90° block motion in accordance with an illustrative embodiment. Fig. 37B depicts 180° block motion in accordance with an illustrative embodiment. Fig. 37C is a two-dimensional (2D) projection of rhombic dodecahedron rotation (hexagon) in accordance with an illustrative embodiment. As shown, cubes require two kinds of inherently difficult rolling / rotational motions (90° and 180°) to move about each other, and can incur considerable sliding friction against any cubes perpendicular to the axis of rotation. Rhombic dodecahedra, in contrast, require only a single simple rotational movement (120°) and eliminate the need for any part of the cells to slide against each other. Rhombic dodecahedra also preserv e a beneficial property of cubes as follows: once two faces of two cells are aligned and connected, all rotations about one of the four shared edges will result in another pair of aligned faces.

[0112] The design and construction of rhombic dodecahedron robotic cells is described below. In one embodiment, the robotic system can include both active cells (that initiate locomotion) and passive cells (that respond to locomotion initiated by an active cell). In the following figures, passive cells are shaded and active cells are white. In an illustrative embodiment, both active cells and passive cells include a hollow plastic dodecahedral shell (H in Fig. 38) with four circular indentations on each face. Inside each indentation a neodymium magnet can be inserted and glued or otherwise secured in place. Passive cells were formed as a single piece of PLA plastic. In alternative embodiments, a different ty pe of magnet may be used and / or a different method of securing the magnets to the shell may be used, such as a friction fit slot, a hook / latch system, etc. In another alternative embodiment, instead of magnets the system may use another method to temporarily attach cells to one another, such as hook and loop tape (i.e., Velcro®), etc. The cells can be made using 3D printing, molding, injection molding, etc.

[0113] Fig. 38 is an exploded view of a rhombic dodecahedral robotic cell in accordance with an illustrative embodiment. As shown, each active cell includes a hexagonal printed circuit board (PCB) (A) as a structural foundation and to create all electrical connections, an analog ON / OFF switch (B) for simple mode control, an eccentric rotating mass (ERM) motor (C) to provide mechanical energy to the morphological system, al 00 mAh LiPo battery' cell(D) with high discharge capabilities, surface mounted light emitting diodes (LEDs) (E) to indicate an active cell’s current status, a three-dimensional (3D) printed PCB mount (F) to hold components in place and mount outer shells, M2 heat inserts (G) to mount the outer shells, outer shells (H) with 48 face-embedded magnets, and M2 screws (I) to complete cell assembly. In alternative embodiments, fewer, additional, and / or different elements may be included in a robotic cell. For example, a different type of motor may be used, a different size / type battery may be used, additional or fewer magnets may be used, etc.

[0114] As shown in Fig. 38, active cells contain a hand-soldered hexagonal printed- circuit-board (PCB), an eccentric rotating mass (ERM) vibration motor, and a 3.7V lOOmAh rechargeable LiPo battery mounted to the outer shell. The outer shell can be formed in a first portion and a second portion which are screwed together or otherwise connected to one another. The analog PCB has an ON / OFF toggle switch and four lights that indicate whether it is in the ON state (blue light) or OFF state (red light). When switched ON, the motor rotates at 19000 RPM consuming 195 mA, which allows for a total of ~25 min of continuous operation (approximately half a million revolutions) before depleting its rechargeable battery. Each active module costs less than $10 USD to build, with the most expensive component being the magnets.

[0115] In another illustrative embodiment, the system can utilize genderless passive magnetic docking, which allows any two cells to dock at any aligned face, without rotations. Genderless passive docking is achieved by arranging and embedding axially-poled neodymium magnets into the outer shell of each the robotic cells used in the system. Fig. 39A depicts symmetry lines about which magnets are mounted on the rhombic dodecahedron robotic cells in accordance with an illustrative embodiment. As shown, the magnet arrangement takes advantage of the symmetry lines that are positioned along the long axis of the rhombic faces of the cells. Fig. 39B depicts a jig that was designed and 3D printed to simplify cell assembly in accordance with an illustrative embodiment. The jig includes a base (Bl) to hold and supply magnets, a slider base (B2) with identical magnet configurations as shown in A that automatically loads itself when slid through the base, and a slider top (B3) that can be removed to allow all four magnets in a cell face to be embedded simultaneously. In alternative embodiments, a different type of jig and / or a different assembly process may be used.

[0116] Initial prototypes incorporated diametrically -poled neodymium magnets that could freely rotate into the necessary orientation to enable cell-cell docking. However, the scale and shape of the cells caused the orientation of magnets to lock pole-to-pole within the cell, which prevented the magnets from rotating and thus inhibited the cell from docking with another. To rectify this, four axially-poled neodymium magnets were embedded on each of the cell’s 12 faces (48 total magnets per cell). In alternative embodiments, a different number of magnets may be used.

[0117] Four unique morphologies including both active and passive cells were configured manually and tested for their locomotive ability. Six trials were recorded, each lasting 1 minute. At the beginning of each trial, the body was placed at a marked central location with the same initial orientation. To isolate the influence of motor orientation from that of bodyshape and motor position, the active cells were rotated to different random orientations for each trial, changing the orientation and directionality of the ERM motor within them.

[0118] Fig. 40 depicts various robotic crystals (or structures) formed by various numbers of individual rhombic dodecahedron robotic cells. Fig. 40A depicts a single rhombic dodecahedron robotic cell in accordance with an illustrative embodiment. Fig. 40B depicts a structure formed by a pair of rhombic dodecahedron robotic cells in accordance with an illustrative embodiment. Fig. 40C depicts a structure formed by three rhombic dodecahedron robotic cells in accordance with an illustrative embodiment. Fig. 40D depicts a structure formed by four rhombic dodecahedron robotic cells in accordance with an illustrative embodiment. Fig. 40E depicts a structure formed by twelve rhombic dodecahedron robotic cells in accordance with an illustrative embodiment. Fig. 40F depicts a structure formed bytwenty rhombic dodecahedron robotic cells in accordance with an illustrative embodiment. Fig. 40G depicts a structure formed by twenty-two rhombic dodecahedron robotic cells in accordance with an illustrative embodiment. Fig. 40H depicts a structure formed by thirty rhombic dodecahedron robotic cells in accordance with an illustrative embodiment. Fig. 401 depicts a structure formed by thirty -nine dodecahedron robotic cells in accordance with an illustrative embodiment. Fig. 40J depicts a structure formed forty -two rhombic dodecahedron robotic cells in accordance with an illustrative embodiment. Fig. 40K depicts a structure formed by forty-six rhombic dodecahedron robotic cells in accordance with an illustrative embodiment. Fig. 40L depicts a structure formed by forty-eight rhombic dodecahedron robotic cells in accordance with an illustrative embodiment.

[0119] Motion of the bodies was tracked using Blender and extracted for analysis. Tracking boxes within Blender were placed along all of the upwards facing cells of the body, and then joined to track the center of mass. One advantage of the chosen magnet arrangement is that it offers a plethora of markers for motion tracking without the need to add sticker tags. The mirror finish of the magnets can cause issues with light reflections at certain orientation, but the effects of this can be minimized with a sufficient number of tracking markers.

[0120] Fig. 41 depicts locomotion patterns for various robotic designs. Fig. 41A depicts a locomotion pattern for a robotic system with three rhombic dodecahedron robotic cells in accordance with an illustrative embodiment. Fig. 41 B depicts a locomotion pattern for a robotic system with four rhombic dodecahedron robotic cells in accordance with an illustrative embodiment. Fig. 41 C depicts a locomotion pattern for a robotic system with seven rhombic dodecahedron robotic cells in accordance with an illustrative embodiment. Fig. 4 ID depicts a locomotion pattern for a robotic system with ten rhombic dodecahedron robotic cells in accordance with an illustrative embodiment. As shown, locomotion behavior was tracked for four different designs across six independent trials. Each design’s center of mass was tracked over evaluation period of 1 minute. The initial orientation for each trial — the top-down view used for motion tracking — as well as a side view of each morphology, is shown for each respective design in Figs. 41 A-41D. The origin of each trial is marked with a dot. Active cells (white) were rotated into six different random orientations, one for each trial, to understand the influence of motor orientation on behavior. In smaller body plans (e.g., Fig. 41A), the orientation of active cells were found to have greater influence on behavior (e.g. the direction of rotation) when compared to larger bodies (e.g. Figs. 41C and 41D). Various correlations between the type of surface contact for a given design were also identified. For example, point contacts tend to produce a high rate of rotation as shown in Fig. 41A, edge contacts produced large, sweeping rotations as shown in Figs. 41B and 41C, and face contact produced mostly translational motion as shown in Fig. 4 ID.

[0121] With these four unique morphologies, several distinct behaviors emerged. Fig. 42 depicts a table that summarizes morphological and behavioral characterization of the designs from Fig. 41 in accordance with an illustrative embodiment. Design A (Fig. 41A) was the smallest morphology' tested, and included just three cells: tw o passive and one active. The robotic system was extremely motile, traveling a mean distance of 126 cm ± 34 standard deviation (SD) over the six trials. However, the motion was largely rotational rather than translational, resulting in a mean net displacement of 6 cm ± 4 SD. The direction of rotation,clockwise or counterclockwise, was greatly influenced by the orientation of the motor within the passive cell. Out of the six trials. 66.67% random rotations of the single active cell caused Design A to turn clockwise, and in the other 33.33% it turned counterclockwise.

[0122] The design of Fig. 41B is also quite small (three passive cells, one active cell) and is also very sensitive to motor orientation. Exactly half of the random rotations applied to its single active cell caused the design of Fig. 41B to turn clockwise, and in the other half of the trials it turned counterclockwise. The system of Fig. 41C includes five passive cells and two active cells. Similar to the design of Fig. 41 A. the design of Fig. 41C was highly mobile, traveling an average of 106 cm ± 22 SD across the six trials. However, contrary to the inconsistent direction of rotation exhibited by the first design, the system in Fig. 41C consistently traveled in a counterclockwise direction of rotation in all six of the trials. This may imply that as the number of cells within a given morphology grows, the orientation of the motor within the active cells has less influence on the overall behavior. Thus, the behavior increasingly becomes a result of the position of active and passive cells.

[0123] The design of Fig. 41 D exhibited mostly translational motion, with a mean distance of travel of 79 cm ± 26 SD, and a mean net displacement of 16 cm ± 10 SD. With seven passive cells and three active cells, Design D was the largest of the four designs tested. In alternative embodiments, different numbers of active and passive cells may be used. In one embodiment, all of the cells may be active. In another embodiment, all of the cells may be passive (i.e., non-robotic) as discussed above.

[0124] In the majority of trials, the design of Fig. 41D moved translationally. Another characteristic of interest is the type of surface contact that a given morphology maintains with the ground plane. Due to the geometrical properties of the rhombic dodecahedron, all cells with a given morphology’ have identical orientations. As a result, each design can have only a single type of surface contact: point, edge, or face. Within the four designs constructed, each of these types of contact were tested. Design A maintained point contact with the ground, and also exemplified the largest rate of consistent rotation, regardless of direction. Designs B and C both maintained edge contact. Their behavior, as with Design A, was characteristically rotational, but with larger, sweeping paths. Design D. on the other hand, maintained face contact with the ground plane and displayed more consistent translational motion. These results suggest that the type of surface contact is not only influential on the emergentbehavior of a morphology, but that it is a trait that can be intentionally modified in a design to influence its behavior.

[0125] Thus, described herein is a non-cubic space- filling building block system that can be formed into a robotic system in one embodiment. The rhombic dodecahedron was used as the building block shape for cells of the robotic system, however any of the other shapes described herein may be used in alternative embodiments. Active cells of the system include a motor that enables system locomutation. In some embodiments, active cells (or passive cells) can also include sensing, computation, and communication components inside the shell of each module. Additionally, internal mechanisms, such as a flywheel and brakes, could be included in the active cells to provide for six axes of rotation instead of three. Cells can also be built with materials that support active de / magnetization of the mounted magnets and that respond to external forces such as light and rotating magnetic fields to allow the cells to passively roll up and down the robot’s body.

[0126] As noted, in one embodiment, a computing system can be used to control the robotic system and / or provide additional features. The computing system can be incorporated into cells of the robotic system. Additionally, one or more components of the computing system may be remote from the robotic system, but in communication with one or more cells of the system. Fig. 43 depicts a computing device 4300 in direct or indirect communication with a network 4335 in accordance with an illustrative embodiment. The computing device 4300 can be incorporated into the robotic cells described herein, or alternatively can be implemented as a standalone controller computer. In alternative embodiments, the computing device 4300 may be in direct communication with another computer (as opposed to networked communication) such as a cell phone, tablet, laptop computer, another robotic cell, etc.

[0127] The computing device 4300 includes a processor (or microcontroller) 4305. an operating system 4310, a memory 4315, an input / output (I / O) system 4320, a network interface 4325, and a robotic application 4330. In alternative embodiments, the computing device 4300 may include fewer, additional, and / or different components. The components of the computing device 4300 communicate with one another via one or more buses or any other interconnect system.

[0128] The processor 4305 of the computing device 4300 can be in electrical communication with and used to control any of the system components described herein,such as motors, switches, etc. The processor 4305 can be any type of computer processor known in the art. and can include a plurality of processors and / or a plurality of processing cores. The processor 4305 can include a controller, a microcontroller, an audio processor, a graphics processing unit, a hardware accelerator, a digital signal processor, etc. Additionally, the processor 4305 may be implemented as a complex instruction set computer processor, a reduced instruction set computer processor, an x86 instruction set computer processor, etc. The processor 4305 is used to run the operating system 4310. which can be a custom operating system specific to the requirements of the proposed system.

[0129] The operating system 4310 is stored in the memory 4315, which is also used to store programs, robotic data, algorithms, network and communications data, peripheral component data, and other operating instructions. The memory 4315 can be one or more memory systems that include various types of computer memory such as flash memory’, random access memory (RAM), dynamic (RAM), static (RAM), a universal serial bus (USB) drive, an optical disk drive, a tape drive, an internal storage device, anon-volatile storage device, a hard disk drive (HDD), a volatile storage device, etc.

[0130] The I / O system 4320, or user interface, is the framework which enables users (and peripheral devices) to interact with the computing device 4300. The I / O system 4320 can include one or more keys or a keyboard, one or more buttons, one or more displays, a speaker, a microphone, etc. that allow the user to interact with and control the computing device 4300. The I / O system 4320 also includes the on / off switch, LED indicator lights, etc. The I / O system 4320 further includes circuitry' and a bus structure to interface with peripheral computing components such as power sources, sensors, etc.

[0131] The network interface 4325 includes transceiver circuitry’ that allows the computing device 4300 to transmit and receive data to / from other devices such as user device(s), remote computing systems, other robots, servers, websites, etc. The network interface 4325 enables communication through the network 4335, which can be one or more communication networks. The network 4335 can include a cable network, a fiber network, a cellular network, a wi-fi network, a landline telephone network, a microwave network, a satellite network, etc. The network interface 4325 also includes circuitry to allow device-to- device communication such as near field communication (NFC), Bluetooth® communication, etc.

[0132] The robotic application 4330 can include hardware, software, and algorithms (e.g., in the form of computer-readable instructions) which, upon activation or execution by the processor 4305, performs any of the various operations described herein such as controlling a motor to move a single cell, controlling coordinated movement of the mobile platform formed by a plurality of cells, monitoring battery life, receiving sensed data, performing analyses of received data, generating control signals, transmitting test result data for remote processing, etc. The robotic application 4330 can utilize the processor 4305 and / or the memory 4315 as discussed above.

[0133] The systems described herein have a myriad of applications. For example, the system can be used as a reconfigurable robotic system. With the capability to move, whether in a lattice of like modules or on its own, each of these modules have the ability to reconfigure around neighboring modules with applications for small scale shape approximation, exploration of small spaces for search and rescue, dynamic support structures, etc.

[0134] The proposed system can also be used to implement reconfigurable household products. For example, a set of hundreds (or thousands) of these modules can be controlled to make temporary7structures for aiding in everyday tasks. These structures can include a step stool for reaching the top shelf of the kitchen cabinets that can stop you from falling, an extra chair for your house guests that perfectly conforms to their body, a dynamic playpen that can move to block off areas with a mobile toddler, a book stand to hold a recipe book while cooking, etc. In another embodiment, the system (whether active or passive) can be used to implement a puzzle. For example, various faces of the blocks can include portions of an image such that when all of the blocks are combined correctly7the entire image can be seen.

[0135] The system can also be used as a tangible interface for dynamic light displays. For example, each of the building blocks can contains one or more LEDs that when arranged by users, or on their own, can be a unique platform for creating 3D dynamic light displays. Cells of the system can also be used to implement self-healing combat protection. For example, groups of these cells can be deployed in combat situations to dynamically shield troops from enemy fire as they are positioned in a single location, or on the move. When damaged, new modules can be deployed fill in gaps as needed. Additionally, surfaces of the modules can be controlled to provide active camouflage within any environment.

[0136] The proposed system can also be used for active 3D modeling as it is able to provide virtually instantaneous modeling of a constructed design. As such, the system can be used as a two-way 3D modeling interface. One can start building a model using representations of the modules on a custom user interface, and the modules can then immediately configure in the same shape for instant, tangible feedback on the design. In the opposite direction, the modules can be hand-configured to build 3D models that can then be further modified in 3D modeling software. The system can further be used for toys, construction materials, furniture, artistic substrates, educational tools for spatial development and learning about geometry', crystals, robots, and evolution, etc.

[0137] The word "illustrative" is used herein to mean serving as an example, instance, or illustration. Any aspect or design described herein as "illustrative" is not necessarily to be construed as preferred or advantageous over other aspects or designs. Further, for the purposes of this disclosure and unless otherwise specified, "a" or "an" means "one or more.”

[0138] The foregoing description of illustrative embodiments of the invention has been presented for purposes of illustration and of description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed, and modifications and variations are possible in light of the above teachings or may be acquired from practice of the invention. The embodiments were chosen and described in order to explain the principles of the invention and as practical applications of the invention to enable one skilled in the art to utilize the invention in various embodiments and with various modifications as suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims appended hereto and their equivalents.

Claims

WHAT IS CLAIMED IS:1 . A construction block system comprising: a shell, wherein the shell forms a cell of the system; and one or more magnets embedded in each of the exterior sides of the shell, wherein the one or more magnets are mounted such that magnets along opposing faces of aligned cells have opposite poles.

2. The system of claim 1, wherein the shell is in the shape of a rhombic dodecahedron.

3. The system of claim 2, wherein the shell includes a first portion and a second portion that are mounted to one another to form the rhombic dodecahedron.

4. The system of claim 1, wherein the magnets comprise axially-poled neodymium magnets.

5. The system of claim 1, wherein the cell includes twelve faces, and wherein each face of the cell includes at least 4 magnets.

6. The system of claim 1. wherein the one or more magnets comprises a single multipole magnet.

7. The system of claim 6, wherein the single multi-pole magnet has eight poles.

8. The system of claim 6, wherein the single multi-pole magnet includes an upper layer and a lower layer.

9. The system of claim 8. wherein the upper layer includes first magnetic portions that alternative between north pole areas and south pole areas.

10. The system of claim 9, wherein the lower layer includes second magnetic portions that alternative between north pole areas and south pole areas.

11. The system of claim 10, wherein the first magnetic portions of the upper layer and second magnetic portions of the lower layer are stacked such that opposing poles are stacked adjacent to one another.

12. The system of claim 1, wherein the one or more magnets includes a dipole magnet positioned about each symmetry line on each exterior side of the block.

13. The system of claim 12, wherein each symmetry’ line originates from a comer formed by the exterior side of the block.

14. A method of forming a construction block system, the method comprising: forming a shell that is a cell of the system; and embedding one or more magnets in each of the exterior sides of the shell, wherein the one or more magnets are mounted such that magnets along opposing faces of aligned cells have opposite poles.

15. The method of claim 14, wherein forming the shell comprises forming the cell in the shape of a rhombic dodecahedron.

16. The method of claim 14, wherein the one or more magnets comprise axially-poled neodymium magnets.

17. The method of claim 14, wherein the cell includes twelve faces, and wherein each face of the cell includes at least 4 magnets.

18. The method of claim 14, wherein embedding the one or more magnets comprises embedding a single multi-pole magnet in each of the exterior sides of the shell.

19. The method of claim 18, wherein the single multi-pole magnet has eight poles.

20. The method of claim 18, wherein the single multi-pole magnet includes an upper layer and a lower layer, wherein the upper layer includes first magnetic portions that alternative between north pole areas and south pole areas, and wherein the lower layer includes second magnetic portions that alternative between north pole areas and south pole areas.

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