Three Dimensional Polyhedral Array

Abstract

A polyhedral array comprises a plurality of discrete polyhedrons and a connection network comprising connections that connect the polyhedrons. The discrete polyhedrons are spaced apart from each other at equilibrium in a predetermined generally regular pattern, and each polyhedron is comprised of edges, faces and vertices. The connection network at least partially constrains the discrete polyhedrons relative to each polyhedron's six degrees of freedom. In some embodiments, the connections extend along the bias of the array. In other embodiments, the connections extend along radial directions. All implementations can be constructed as regular arrays or in lattice networks.

1 . A polyhedral array, comprising:
 a plurality of discrete polyhedrons that are spaced apart from each other at equilibrium in a predetermined generally regular pattern, each polyhedron being comprised of edges, faces and vertices; and   a connection network comprising connections extending along bias directions to connect the polyhedrons;   wherein the connection network at least partially constrains the discrete polyhedrons with respect to each polyhedron's six degrees of freedom.   
   
   
       2 . The array of  claim 1 , wherein each polyhedron's six degrees of freedom are defined as the ability to translate in the X, Y and/or Z directions of a coordinate reference frame, and the ability to rotate about the X, Y and/or Z directions. 
   
   
       3 . The array of  claim 1 , wherein the polyhedrons are arranged in multiple, generally parallel layers. 
   
   
       4 . The array of  claim 1 , wherein at least some of the plurality of polyhedrons generally occupy a first plane, and wherein the bias directions along which the connections extend intersect the first plane. 
   
   
       5 . The array of  claim 3 , wherein the bias directions are oriented at angles of approximately 45 degrees to the first plane. 
   
   
       6 . The array of  claim 1 , wherein the polyhedrons are arranged in multiple layers, and wherein the bias directions along which the connections extend are inclined at about 45 degrees relative to an expected direction of a resolved load on the array. 
   
   
       7 . The array of  claim 1 , wherein at least one of the connections extends between an edge of a first of the polyhedrons and an edge of a second of the polyhedrons. 
   
   
       8 . The array of  claim 1 , wherein at least one of the connections extends between a face of a first of the polyhedrons and a face of a second of the polyhedrons. 
   
   
       9 . The array of  claim 1 , wherein at least one of the connections extends between a vertex of a first of the polyhedrons and a vertex of a second of the polyhedrons. 
   
   
       10 . The array of  claim 1 , wherein at least one of the connections extends between one of a group consisting of a face, an edge and a vertex of a first polyhedron, and a different one of the group consisting of a face, an edge and a vertex of a second polyhedron. 
   
   
       11 . The array of  claim 1 , wherein the array is coherent. 
   
   
       12 . The array of  claim 1 , wherein the array is omni-extensible. 
   
   
       13 . The array of  claim 1 , wherein an existing array can be increased in size by connecting additional discrete polyhedrons to existing discrete polyhedrons with additional connections without other modifications to the existing array. 
   
   
       14 . The array of  claim 1 , wherein each discrete polyhedron is a finitely closed structure having structural integrity independent of the respective connections to which said discrete polyhedron is connected and independent of other discrete polyhedrons in the array. 
   
   
       15 . The array of  claim 1 , wherein the interconnecting network is configured in a generally repeating pattern. 
   
   
       16 . The array of  claim 1 , wherein the connections comprise at least one of mechanical elements, bonds or guest molecules, ligands and ligatures. 
   
   
       17 . The array of  claim 1 , wherein the connections comprise mechanical elements that have greater resiliency than the polyhedrons. 
   
   
       18 . The array of  claim 1 , wherein the connections are mechanical elements comprising spring-shaped portions. 
   
   
       19 . The array of  claim 1 , wherein each polyhedron occupies a unique location at equilibrium that can be specified with Cartesian coordinates. 
   
   
       20 . The array of  claim 1 , wherein the array is anisotropic, with at least one polyhedron having specific properties different from another of the plurality of polyhedrons. 
   
   
       21 . The array of  claim 1 , wherein at least one of the connections can have predetermined properties different from another of the connections. 
   
   
       22 . The array of  claim 1 , wherein at least one of the connections has a property that varies along its length. 
   
   
       23 . The array of  claim 1 , wherein the discrete polyhedrons comprise a first material and the connections comprise a second material different from the first material. 
   
   
       24 . The array of  claim 1 , wherein at least one of the plurality of polyhedrons comprises a closed polyhedron having a majority of closed faces. 
   
   
       25 . The array of  claim 1 , wherein at least one of the plurality of polyhedrons comprises an open polyhedron each having a majority of open faces. 
   
   
       26 . The array of  claim 1 , wherein the plurality of polyhedrons comprises at least one interiorly hollow polyhedron. 
   
   
       27 . The array of  claim 1 , wherein the plurality of polyhedrons comprises at least one solid polyhedron. 
   
   
       28 . The array of  claim 1 , wherein each polyhedron satisfies the condition of having a face, an edge or a vertex approximately coincident with one of the six sides of a cube circumscribing the polyhedron. 
   
   
       29 . The array of  claim 1 , wherein the polyhedrons are selected from the list consisting of cubes, icosahedrons, truncated cubes, truncated octahedrons, truncated icosahedrons, cubo-octahedrons, dodecahedrons, truncated dodecahedrons, icosidodecahedrons, rombicosidodecahedrons, snub dodecahedrons, truncated cubo-octahedrons, stellated forms, deltahedrals and dual tetrahedrals. 
   
   
       30 . The array of  claim 1 , wherein at least one of the polyhedrons is formed of two halves. 
   
   
       31 . The array of  claim 30 , wherein the polyhedron is an icosahedron and has a geodesic saw tooth-shaped equator defining the two halves. 
   
   
       32 . The array of  claim 1 , wherein at least one of the connections extends continuously from a first polyhedron, to a second polyhedron and to an nth polyhedron. 
   
   
       33 . The array of  claim 1 , wherein at least some of the connections are compression members configured primarily to resist compression forces. 
   
   
       34 . The array of  claim 1 , wherein the predetermined regular pattern in which the polyhedrons are arranged can include spaces occurring at generally regular uniform intervals. 
   
   
       35 . The array of  claim 1 , wherein at least some of the polyhedrons are icosahedrons. 
   
   
       36 . The array of  claim 1 , wherein the plurality of polyhedrons includes at least one interior polyhedron connected to twelve adjacent polyhedrons. 
   
   
       37 . The array of  claim 1 , wherein the discrete polyhedrons can move relative to each other in response to applied loads, but remain spaced apart from each other at equilibrium and within a selected working load range. 
   
   
       38 . The array of  claim 1 , wherein a force above a predetermined working load range applied to the array can urge two adjacent polyhedrons from an equilibrium position in which the adjacent polyhedrons are separated from each other into an under load position in which the adjacent polyhedrons are in contact with each other. 
   
   
       39 . A polyhedral array, comprising:
 a plurality of discrete polyhedrons that are spaced apart from each other at equilibrium in a predetermined generally regular pattern, each polyhedron being comprised of edges, faces and vertices; and   a connection network interconnecting the discrete polyhedrons, the connection network comprising radial connections, wherein a first end of each radial connection and a corresponding first connection location on one of the polyhedrons occupy a first plane, and wherein a second end of each radial connection and a corresponding second connection location on another of the polyhedrons occupy a second plane that is not parallel to the first plane,   wherein the interconnecting network at least partially constrains the discrete polyhedrons relative to each polyhedron's six degrees of freedom.   
   
   
       40 . The array of  claim 39 , wherein the first and second planes of the respective first and second connection locations are mutually orthogonal. 
   
   
       41 . A polyhedral array, comprising:
 a plurality of discrete polyhedrons that are spaced apart from each other at equilibrium in a generally regular pattern, each polyhedron being comprised of edges, faces and vertices; and   a connection network interconnecting the discrete polyhedrons, the connection network comprising connections having a first end connected in a first plane and a second end connected in a second plane different from the first plane,   wherein the connection network at least partially constrains the discrete polyhedrons relative to three Cartesian axes, and adjacent polyhedrons are oriented in a face to face relationship relative to each other.   
   
   
       42 . The array of  claim 41 , wherein the connections are curved mechanical elements, and wherein each curved mechanical element has a first end connected to a first face of a first polyhedron and a second end connected to a second face of a second polyhedron, the first and second faces occupying different planes. 
   
   
       43 . The array of  claim 41 , wherein when the array is subjected to a load above a predetermined working load range, the array deforms such that at least two of the polyhedrons make face to face contact with each other. 
   
   
       44 . The array of  claim 41 , wherein when the array is subjected to a force or torque above a predetermined working range, the array deforms such that at least one of the polyhedrons undergoes a predetermined transformation in shape. 
   
   
       45 . The array of  claim 44 , wherein the at least one of the polyhedrons is reversibly transformed such that the at least one of the polyhedrons returns to an original shape if the force or torque is removed.