4-Regular vertex-transitive tilings of E³

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.".