Preprint Article Version 1 This version not peer reviewed

Aesthetic Patterns with symmetries of the Regular Polyhedron

Version 1 : Received: 26 January 2017 / Approved: 26 January 2017 / Online: 26 January 2017 (10:35:59 CET)

A peer-reviewed article of this Preprint also exists.

Ouyang, P.; Wang, L.; Yu, T.; Huang, X. Aesthetic Patterns with Symmetries of the Regular Polyhedron. Symmetry 2017, 9, 21. Ouyang, P.; Wang, L.; Yu, T.; Huang, X. Aesthetic Patterns with Symmetries of the Regular Polyhedron. Symmetry 2017, 9, 21.

Journal reference: Symmetry 2017, 9, 21
DOI: 10.3390/sym9020021

Abstract

A fast algorithm is established to transform points of the unit sphere into fundamental region symmetrically. With the resulting algorithm, a flexible form of invariant mappings is achieved to generate aesthetic patterns with symmetries of the regular polyhedra. This method avoids the order restriction of symmetry groups, which can be similarly extended to treat regular polytopes in n-dimensional space for n>=4.

Subject Areas

Regular polyhedra, reflection group, fundamental region, invariant mapping

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