2000 Mathematics Subject Classification. Primary: 51M20; Secondary: 52B15
Combinatorially regular polyhedra in Euclidean 3-space E3 are polyhedral embeddings in
E3 of regular maps (cell-complexes) on orientable compact closed surfaces. Regular maps
on surfaces have been studied from combinatorial, topological, algebraic and geometric
viewpoints for well over 100 years (see Coxeter & Moser ). Combinatorially regular
polyhedra and their underlying topological maps can generally be viewed as higher-genus
analogues of the Platonic
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