Space-Filling Array in √φ Field

sketchfab

A complex geometric structure unfolds as an arrangement of cells within a five-directional system. The primary cell is a Rhombic Icosahedron, a polar zonohedron, which serves as the foundation for this intricate design. Secondary cells, reduced by one or two directions, take the form of Rhombic Dodecahedra and Hexahedra. In this precise system, edge lines intersect at 90 degrees, while others meet at an angle of Arc cos 1/φ, specifically 51.827 degrees. This same set of angles is replicated in dihedral relationships throughout the structure. This array exhibits fivefold symmetry around a central axis and features five planes of reflection that converge on this axis. The model's composition consists solely of square facets, with rhombic facets left intentionally incomplete. This creation was crafted using vZome software.