# 4-Regular Vertex-Transitive Tilings of E 3

Discrete & Computational Geometry, Sep 2000

Abstract. {There exist precisely 149 topological types of semipolytopal tile-transitive tilings of E 3 by extetrahedra'' (obtained from tetrahedra by introducing certain new vertices of degree 2 ). Dualization gives rise to 149 types of 4-regular vertex-transitive tilings. The 4-coordinated networks carried by these tilings are closely related to crystal structures such as zeolites or diamond. These results are obtained using combinatorial tiling theory.''}

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O. Delgado Friedrichs, D. H. Huson. 4-Regular Vertex-Transitive Tilings of E 3, Discrete & Computational Geometry, 2000, 279-292, DOI: 10.1007/s004540010035