The classification of face-transitive periodic three-dimensional tilings
- 1 November 1993
- journal article
- Published by International Union of Crystallography (IUCr) in Acta Crystallographica Section A Foundations of Crystallography
- Vol. 49 (6) , 806-817
- https://doi.org/10.1107/s010876739300354x
Abstract
It has long been known that there exists an infinite number of types of tile-transitive periodic three-dimensional tilings. Here, it is shown that, by contrast, the number of types of face-transitive periodic three-dimensional tilings is finite. The method of Delaney symbols and the properties of the 219 isomorphism classes of crystallographic space groups are used to find exactly 88 equivariant types that fall into seven topological families.Keywords
This publication has 0 references indexed in Scilit: