Graphs and Combinatorics

, Volume 26, Issue 4, pp 537–548 | Cite as

Polyhedral Suspensions of Arbitrary Genus

  • Serge LawrencenkoEmail author
Original Paper


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.


Regular polyhedra Simplicial complexes Planarity Graph embedding Maximum genus 

Mathematics Subject Classification (2000)

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


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Copyright information

© Springer 2010

Authors and Affiliations

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

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