Andreini tessellationThe Andreini tessellations are tilings of three-dimensional space using Platonic and Archimedean solids such that all vertices are identical. There are precisely five such tilings:
- The tiling of cubes
- The tiling of octahedra and cuboctahedra
- The tiling of truncated octahedra
- The tiling of octahedra and tetrahedra
- The tiling of tetrahedra and truncated tetrahedra
This is not correct. There are 28 such tessellations. See B. Grünbaum, Uniform tilings of 3-space. Geombinatorics 4(1994), 49 - 56.