The Classification of Face-Transitive Periodic 3D-Tilings 

Andreas W.M. Dress, Daniel H. Huson and Emil Molnar

Abstract:
It has long been known that there exist an infinite number of types of
tile-transitive periodic 3D-tilings. 
Here it is shown that the number of types of face-transitive
periodic 3D-tilings, however, is finite. 
Using the method of Delaney symbols and properties of the 219 isomorphism
classes of crystallographic space groups,
the authors find exactly 88 equivariant types, that fall into
seven topological families.

Appeared in:
Acta Crystallographica, A49:806--817 (1993)