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Polyhedral suspensions of arbitrary genus. (English) Zbl 1208.57003

A bipyramid is a Euclidean polyhedron with triangular faces such that there exist two non-adjacent vertices each adjacent to the other vertices lying in a same plane, and without self-intersection. The author constructs bipyramids of arbitrary genus. The already known construction in the genus one case is recalled.

MSC:

57M20 Two-dimensional complexes (manifolds) (MSC2010)
05C10 Planar graphs; geometric and topological aspects of graph theory
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
52B05 Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.)
52B70 Polyhedral manifolds
57M15 Relations of low-dimensional topology with graph theory
51M20 Polyhedra and polytopes; regular figures, division of spaces
51M04 Elementary problems in Euclidean geometries
55P40 Suspensions
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References:

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