Spelunking Adventure III: Close-Pack and Space-Fill Octahedral Domains

Curtis Palmer
Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture (2012)
Pages 525–526 Short Papers


Twelve polyhedra with octahedral symmetry are modeled within a unit radius circumsphere. These are used as blocks to populate two matrices that share a 12-around-1 packing strategy: a close-pack array of unit spheres and a rhombic dodecahedral space-fill. Each polyhedron is modeled with a tree of virtual layers containing geometric identifiers: points, point-clouds, vectors, surfaces, and polysurfaces. With programmatic selection of layers a vast number of constructed spaces can be visualized, printed and animated. Visual examples are presented.