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Maximally symmetric polyhedral realizations of Dyck's regular map
Author(s) -
Brehm Ulrich
Publication year - 1987
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300013474
Subject(s) - polyhedron , mathematics , symmetry (geometry) , combinatorics , order (exchange) , symmetry group , geometry , finance , economics
We construct realizations of Dyck's regular map of genus three as polyhedra in ℝ 3 . One of these has one axis of symmetry of order three and three axes of symmetry of order two. The other polyhedra have three axes of symmetry. We show that a polyhedron realizing Dyck's regular map cannot have a symmetry group of order larger than six. Thus the symmetry groups of our realizations are maximal.