Combinatorial 3-Manifolds with 10 Vertices

Combinatorial 3-manifolds with a cyclic automorphism group

In this article we substantially extend the classification of combinatorial 3-manifolds with cyclic automorphism group up to 22 vertices. Moreover, several combinatorial criteria are given to decide, whether a cyclic combinatorial d-manifold can be generalized to an infinite family of such complexes together with a construction principle in the case that such a family exist. In addition, a new ...

Isomorphism-free lexicographic enumeration of triangulated surfaces and 3-manifolds

We present a fast enumeration algorithm for combinatorial 2and 3-manifolds. In particular, we enumerate all triangulated surfaces with 11 and 12 vertices and all triangulated 3-manifolds with 11 vertices. We further determine all equivelar maps on the non-orientable surface of genus 4 as well as all equivelar triangulations of the orientable surface of genus 3 and the non-orientable surfaces of...

Degree-regular triangulations of torus and Klein bottle

A combinatorial 2-manifold is called weakly regular if the action of its automorphism group on its vertices is transitive. A combinatorial 2-manifold is called degree-regular if each of its vertices have the same degree. Clearly, a weakly regular combinatorial 2-manifold is degree-regular. In [5], Lutz has classified all the weakly-regular combinatorial 2-manifolds on at most 15 vertices, among...

Neighborly combinatorial 3-manifolds with 9 vertices

Triangulated Manifolds with Few Vertices: Combinatorial Manifolds