THE CLASSIFICATION OF FACE-TRANSITIVE PERIODIC 3-DIMENSIONAL TILINGS

Authors
DRESS AWM HUSON DH MOLNAR E
Citation
Awm. Dress et al., THE CLASSIFICATION OF FACE-TRANSITIVE PERIODIC 3-DIMENSIONAL TILINGS, Acta crystallographica. Section A, Foundations of crystallography, 49, 1993, pp. 806-817
Citations number
27
Categorie Soggetti
Crystallography
Journal title
Acta crystallographica. Section A, Foundations of crystallography → ACNP
ISSN journal
01087673
Volume
49
Year of publication
1993
Part
6
Pages
806 - 817
Database
ISI
SICI code
0108-7673(1993)49:<806:TCOFP3>2.0.ZU;2-J
Abstract
It has long been known that there exists an infinite number of types o f tile-transitive periodic three-dimensional tilings. Here, it is show n that, by contrast, the number of types of face-transitive periodic t hree-dimensional tilings is finite. The method of Delaney symbols and the properties of the 219 isomorphism classes of crystallographic spac e groups are used to find exactly 88 equivariant types that fall into seven topological families.