Space Fillings tests which polyhedra can tile three-dimensional space without gaps or overlaps. Various polyhedral forms — including rhombic dodecahedra, truncated octahedra, and related types — each present distinct challenges for achieving complete space tessellation.
Face arrangements, edge relationships, and angular constraints determine space-filling capability. Some configurations succeed at local tessellation but fail when extended, while others tile indefinitely from a single unit type. Physical models demonstrate these outcomes directly.
3D printed assemblies allow multiple units to combine, revealing space-filling patterns or exposing geometric limitations through direct observation. The investigation remains ongoing.
Photography: Phillip C. Reiner
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