Neighborly maps with few vertices
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.
scientific article; zbMATH DE number 61214
scientific article