Tiling Space By Platonic Solids I.
Olaf Delgado Friedrichs Daniel H. Huson

Abstract:

There exist precisely 914, 58 and 46 equivariant types of tile-transitive
tilings of 3-dimensional euclidean space by topological cubes, octahedra and
tetrahedra, that fall in to 11, 3, and 9 topological families, respectively.
Representatives are described for all topological families.
A general method for obtaining results of this kind is introduced.


Discrete and Computational Geometry 21:299-315 (1999).