Next Article in Journal
Perlman and Wellner’s Circular and Transformed Circular Copulas are Particular Beta and t Copulas
Previous Article in Journal / Special Issue
A Note on Lower Bounds for Colourful Simplicial Depth
Symmetry 2013, 5(1), 54-80; doi:10.3390/sym5010054
Article

Non-Crystallographic Symmetry in Packing Spaces

1,* , 2
 and
1
Received: 25 November 2012 / Accepted: 5 December 2012 / Published: 9 January 2013
(This article belongs to the Special Issue Polyhedra)
Download PDF [2516 KB, uploaded 9 January 2013]

Abstract

In the following, isomorphism of an arbitrary finite group of symmetry, non-crystallographic symmetry (quaternion groups, Pauli matrices groups, and other abstract subgroups), in addition to the permutation group, are considered. Application of finite groups of permutations to the packing space determines space tilings by policubes (polyominoes) and forms a structure. Such an approach establishes the computer design of abstract groups of symmetry. Every finite discrete model of the real structure is an element of symmetry groups, including non-crystallographic ones. The set packing spaces of the same order N characterizes discrete deformation transformations of the structure.
Keywords: tilings; finite groups of permutations; packing spaces; polyominoes; quaternion group; cayley tables; Pauli matrices; dirac matrices tilings; finite groups of permutations; packing spaces; polyominoes; quaternion group; cayley tables; Pauli matrices; dirac matrices
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Share & Cite This Article

Further Mendeley | CiteULike
Export to BibTeX |
EndNote
MDPI and ACS Style

Rau, V.G.; Lomtev, L.A.; Rau, T.F. Non-Crystallographic Symmetry in Packing Spaces. Symmetry 2013, 5, 54-80.

View more citation formats

Related Articles

Article Metrics

For more information on the journal, click here

Comments

Cited By

[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert