4-Regular Vertex-Transitive Tilings of E 3

{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.'} Received February 12, 1999, and in revised form September 21, 1999. Online publication May 15, 2000.