Graphs and Combinatorics

, Volume 26, Issue 4, pp 537–548

Polyhedral Suspensions of Arbitrary Genus

Original Paper

DOI: 10.1007/s00373-010-0938-5

Cite this article as:
Lawrencenko, S. Graphs and Combinatorics (2010) 26: 537. doi:10.1007/s00373-010-0938-5
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Abstract

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 two-dimensional polyhedron is constructed in four dimensions.

Keywords

Regular polyhedra Simplicial complexes Planarity Graph embedding Maximum genus 

Mathematics Subject Classification (2000)

Primary 57M20 Secondary 05C10 90C57 52B05 52B70 57M15 51M20 51M04 55P40 

Copyright information

© Springer 2010

Authors and Affiliations

  1. 1.Department of MathematicsMoscow Institute of Steel and AlloysMoscowRussia

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