Symmetric vertex- and edge-transitive 3-periodic nets.

Authors

Michael O'Keeffe, Michael M J Treacy

Published in

Acta crystallographica. Section A, Foundations and advances. Sep 01, 2026. Epub Sep 01, 2026.

Abstract

Vertex- and edge-transitive graphs that admit tilings (tessellate graphs) have been known for 20 years. In this paper, we identify additional families of vertex- and edge-transitive graphs with symmetric embeddings, for which the order of the point symmetry at a vertex equals the vertex's coordination number. Remarkably, symmetric tessellate graphs appear over 150 000 times in crystal structures, while there is only one reported occurrence of a symmetric decussate (untessellable) graph.

PMID:
42411320
Bibliographic data and abstract were imported from PubMed on 07 Jul 2026.

Read full publication at:
Please sign in to see all details.

Stats

1-terrible, 9-excellent. How would you rate this publication? Sign in in to submit your rating.

Post a comment

You need to be signed in to post comments. You can sign in here.

Comments

There are no comments yet.