Polyhedral Suspensions of Arbitrary Genus

A new class of polyhedra is discovered—bipyramids of arbitrarily prescribed genus. A two-dimensional generalization of Fáry’s Theorem is established. A purely combinatorial definition of a polyhedral suspension is given. A new regular 2-dimensional polyhedron is constructed in four dimensions. Short running title: Polyhedral suspensions. 2000 AMS Subject Classification: Primary: 57M20; Secondary: 05C10, 90C57, 52B05, 52B70, 57M15, 51M20, 51M04, 55P40. Key words and phrases: regular polyhedra, simplicial complexes, planarity, graph embedding, maximum genus.

• Type: Journal
• Year: 2010
• Where: GC
• Authors: Serge Lawrencenko
• Keywords: Applied Computing, GC 2010, Polyhedral Suspensions, Regular 2-dimensional Polyhedron, Short Running Title