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Geometric realizations of abstract regular polyhedra with automorphism group H. | LitMetric

Geometric realizations of abstract regular polyhedra with automorphism group H.

Acta Crystallogr A Found Adv

Department of Mathematics, Ateneo de Manila University, Katipunan Avenue, Loyola Heights, Quezon City 1108, Philippines.

Published: May 2020

A geometric realization of an abstract polyhedron {\cal P} is a mapping that sends an i-face to an open set of dimension i. This work adapts a method based on Wythoff construction to generate a full rank realization of an abstract regular polyhedron from its automorphism group Γ. The method entails finding a real orthogonal representation of Γ of degree 3 and applying its image to suitably chosen (not necessarily connected) open sets in space. To demonstrate the use of the method, it is applied to the abstract polyhedra whose automorphism groups are isomorphic to the non-crystallographic Coxeter group H.

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Source
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7233025PMC
http://dx.doi.org/10.1107/S2053273320001564DOI Listing

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