Periodic Corpuscle Structures and the Spaces in Between

Corpuscles are flexible geometric elements formed by regular triangles. Corpuscle elements can be joined, thus serving as building blocks for polyhedral chains and complex threedimensional structures. Here we describe a periodic three-dimensional corpuscle grid whose negative space consists of periodically arranged octahedra. As a recurrent local structure, the grid contains the octahedron-centric corpuscle ball, an arrangement of 18 corpuscle elements surrounding an empty, octahedron-shaped space. Similarly, we construct corpuscle balls with empty cubes or icosahedra at their centres and the according rotation symmetries. Both corpuscle balls can be extended to form periodic grids, but only if slight deformations of the edge lengths are allowed. The corpuscle grids and balls contain rigid, ring-like substructures, which stabilise them against deformation.