There are five convex polyhedra that can tile 3D space by translation only (sliding them into place without rotating or flipping). These are sometimes called the “Fedorov Solids” or “Fedorov Five”, and are listed below:
- Cube
- Hexagonal Prism
- Rhombic Dodecahedron
- Elongated Dodecahedron
- Truncated Octahedron
The previous video looked at 3D cellular automata with expanded (Lp-ball) neighborhoods specifically for the cubic honeycomb case. This video looks at 3D cellular automata with Lp-ball neighborhoods on the remaining four honeycombs. In all cases p=2. Larger Lp-ball neighborhoods tend to produce more intricate fractal-like forms.
Related Work
- Francis A. Bitonti, Ed Pegg Jr (2008), Rhombic Dodecahedra Totalistic Cellular Automaton
- Francis A. Bitonti (2011), Hexagonal Prism Totalistic Cellular Automaton
- Francis A. Bitonti, Ed Pegg Jr (2011), Truncated Octahedra Outer Totalistic Cellular Automaton
- pataphysical (2016), Cellular Automata with Spherical Close-packing Geometry
- Radhika Prasad (2020), [WSS20] Cellular Automata (CA) on 3D Lattices