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Altshuler, Amos; Brehm, Ulrich

Neighborly maps with few vertices. (English) Zbl 0756.52014

Discrete Comput. Geom. 8, No. 1, 93-104 (1992).
The authors present an exhausting and computer-aided list of all triangulations of closed surfaces which have less than 12 vertices and which are neighborly meaning that any pair of vertices is joined by an edge. This concerns the cases of \(n=4,6,7,9\), or 10 vertices. It is found that there are exactly one triangulation for \(n=4,6\) or 7, two triangulations for \(n=9\), and 14 combinatorially distinct triangulations for \(n=10\), among them a very symmetric one with an icosahedral automorphism group. It occurs as a modification of the hemidodecahedron.
Reviewer: W.Kühnel (Duisburg)

Cited in 6 Documents

MSC:

52B70 Polyhedral manifolds
52B55 Computational aspects related to convexity
57Q15 Triangulating manifolds
05C10 Planar graphs; geometric and topological aspects of graph theory

Keywords:

triangulations of closed surfaces; less than 12 vertices; neighborly
PDFBibTeX XMLCite
\textit{A. Altshuler} and \textit{U. Brehm}, Discrete Comput. Geom. 8, No. 1, 93--104 (1992; Zbl 0756.52014)
Full Text: DOI

References:

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