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The polytopes of the H 3 group with 60 vertices and their orbit decompositions
Author(s) -
Bourret Emmanuel,
Grabowiecka Zofia
Publication year - 2019
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.742
H-Index - 83
ISSN - 2053-2733
DOI - 10.1107/s2053273319000640
Subject(s) - coxeter group , polytope , combinatorics , icosahedral symmetry , mathematics , group (periodic table) , diagram , reflection (computer programming) , orbit (dynamics) , crystallography , geometry , physics , chemistry , computer science , quantum mechanics , statistics , programming language , engineering , aerospace engineering
The goal of this article is to compare the geometrical structure of polytopes with 60 vertices, generated by the finite Coxeter group H 3 , i.e. an icosahedral group in three dimensions. The method of decorating a Coxeter–Dynkin diagram is used to easily read the structure of the reflection‐generated polytopes. The decomposition of the vertices of the polytopes into a sum of orbits of subgroups of H 3 is given and presented as a `pancake structure'.