Abstract: A truncated icosahedron assembly can include a plurality of structural elements coupled together in a truncated icosahedral configuration. Each structural element can include first and second hexagonal portions and first and second pentagonal portions. The hexagonal portions of each structural element can be coupled together at a first edge of the first hexagonal portion and a second edge of the second hexagonal portion. The pentagonal portions of each structural element can be spaced relative to each other by the first and second hexagonal portions. The first pentagonal portion of each structural element can be coupled to the hexagonal portions adjacent the first edge of the first hexagonal portion and the second edge of the second hexagonal portion. The second pentagonal portion of each structural element can be coupled to the hexagonal portions adjacent the first edge of the first hexagonal portion and the second edge of the second hexagonal portion.

Abstract: A truncated icosahedron assembly can include a plurality of structural elements coupled together in a truncated icosahedral configuration. Each structural element can include first and second hexagonal portions and first and second pentagonal portions. The hexagonal portions of each structural element can be coupled together at a first edge of the first hexagonal portion and a second edge of the second hexagonal portion. The pentagonal portions of each structural element can be spaced relative to each other by the first and second hexagonal portions. The first pentagonal portion of each structural element can be coupled to the hexagonal portions adjacent the first edge of the first hexagonal portion and the second edge of the second hexagonal portion. The second pentagonal portion of each structural element can be coupled to the hexagonal portions adjacent the first edge of the first hexagonal portion and the second edge of the second hexagonal portion.

Abstract: An array comprises a plurality of ring elements and a plurality of mortar elements. The ring elements comprise polyhedroids interconnected to one another to form a closed ring shape, with the polyhedroids having a generally polyhedral shape. The mortar elements are configured to connect ring elements to each other.

Abstract: An array comprises a plurality of ring elements and a plurality of mortar elements. The ring elements comprise polyhedroids interconnected to one another to form a closed ring shape, with the polyhedroids having a generally polyhedral shape. The mortar elements are configured to connect ring elements to each other.

Abstract: A structural fabric comprises a plurality of discrete and spaced apart icosahedral elements and a plurality of interconnecting elements. The icosahedra elements are interconnected at selected edges by the interconnecting elements in tension so as to form a self-supported array of the icosahedral elements. The icosahedral elements may be icosahedrons (20 sides) or truncated icosahedrons (32 sides). Methods of constructing the structural fabric are also disclosed.

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.