3,393 research outputs found
Triangulated Manifolds with Few Vertices: Centrally Symmetric Spheres and Products of Spheres
The aim of this paper is to give a survey of the known results concerning
centrally symmetric polytopes, spheres, and manifolds. We further enumerate
nearly neighborly centrally symmetric spheres and centrally symmetric products
of spheres with dihedral or cyclic symmetry on few vertices, and we present an
infinite series of vertex-transitive nearly neighborly centrally symmetric
3-spheres.Comment: 26 pages, 8 figure
Small examples of non-constructible simplicial balls and spheres
We construct non-constructible simplicial -spheres with vertices
and non-constructible, non-realizable simplicial -balls with vertices
for .Comment: 9 pages, 3 figure
Combinatorial 3-manifolds with 10 vertices
We give a complete enumeration of all combinatorial 3-manifolds with 10
vertices: There are precisely 247882 triangulated 3-spheres with 10 vertices as
well as 518 vertex-minimal triangulations of the sphere product
and 615 triangulations of the twisted sphere product S^2_\times_S^1.
All the 3-spheres with up to 10 vertices are shellable, but there are 29
vertex-minimal non-shellable 3-balls with 9 vertices.Comment: 9 pages, minor revisions, to appear in Beitr. Algebra Geo
One-Point Suspensions and Wreath Products of Polytopes and Spheres
It is known that the suspension of a simplicial complex can be realized with
only one additional point. Suitable iterations of this construction generate
highly symmetric simplicial complexes with various interesting combinatorial
and topological properties. In particular, infinitely many non-PL spheres as
well as contractible simplicial complexes with a vertex-transitive group of
automorphisms can be obtained in this way.Comment: 17 pages, 8 figure
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