4-Regular Vertex-Transitive Tilings of E3

Abstract. {There exist precisely 149 topological types of semipolytopal tile-transitive tilings of E3 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.''}