Abstract.
There exist precisely 914, 58, and 46 equivariant types of tile-transitive tilings of three-dimensional euclidean space by topological cubes, octahedra, and tetrahedra, that fall into 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.
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Received February 13, 1997, and in revised form September 17, 1997.
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Delgado Friedrichs, O., Huson, D. Tiling Space by Platonic Solids, I . Discrete Comput Geom 21, 299–315 (1999). https://doi.org/10.1007/PL00009423
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DOI: https://doi.org/10.1007/PL00009423