Submitted:
26 January 2017
Posted:
26 January 2017
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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.
Keywords:
Regular polyhedra
; reflection group
; fundamental region
; invariant mapping
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