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Ordering of convex polyhedra and the Fedorov algorithm

Ordering of convex polyhedra and the Fedorov algorithm A method of naming any convex polyhedron by a numerical code arising from the adjacency matrix of its edge graph has been previously suggested. A polyhedron can be built using its name. Classes of convex n‐acra (i.e. n‐vertex polyhedra) are strictly (without overlapping) ordered by their names. In this paper the relationship between the Fedorov algorithm to generate the whole combinatorial variety of convex polyhedra and the above ordering is described. The convex n‐acra are weakly ordered by the maximum extra valencies of their vertices. Thus, non‐simple n‐acra follow the simple ones for any n. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Crystallographica Section A Foundations of Crystallography Wiley

Ordering of convex polyhedra and the Fedorov algorithm

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References (4)

Publisher
Wiley
Copyright
Copyright © 2017 Wiley Subscription Services, Inc., A Wiley Company
ISSN
0108-7673
eISSN
1600-5724
DOI
10.1107/S2053273316017095
pmid
28042807
Publisher site
See Article on Publisher Site

Abstract

A method of naming any convex polyhedron by a numerical code arising from the adjacency matrix of its edge graph has been previously suggested. A polyhedron can be built using its name. Classes of convex n‐acra (i.e. n‐vertex polyhedra) are strictly (without overlapping) ordered by their names. In this paper the relationship between the Fedorov algorithm to generate the whole combinatorial variety of convex polyhedra and the above ordering is described. The convex n‐acra are weakly ordered by the maximum extra valencies of their vertices. Thus, non‐simple n‐acra follow the simple ones for any n.

Journal

Acta Crystallographica Section A Foundations of CrystallographyWiley

Published: Jan 1, 2017

Keywords: ; ; ; ;

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