Geometric realizations of abstract regular polyhedra with automorphism group H3

• Main Authors: Loyola, Mark L, Aranas, Jonn Angel L
• Format: text
• Published: Archīum Ateneo 2020
• Subjects: abstract regular polyhedra; geometric realizations; non-crystallographic Coxeter group H3; string C-groups; Geometry and Topology; Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/143; https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1142&context=mathematics-faculty-pubs
• Institution: Ateneo De Manila University

A geometric realization of an abstract polyhedron 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 Gamma. The method entails fin...