Partitioning the triangles of the cross polytope into surfaces

Details Partitioning the triangles of the cross polytope into surfaces Partitioning the triangles of the cross polytope into surfaces

2010-09-14

arxiv.org/abs/1009.2642v2

Mathematics

Combinatorics

13 pages, 1 figure

Scientific paper

We present a constructive proof, that there exists a decomposition of the 2-skeleton of the k-dimensional cross polytope \beta^k into closed surfaces of genus \leq 1, each with a transitive automorphism group given by the vertex transitive Z_{2k}-action on \beta^k. Furthermore we show, that for each k \equiv 1,5(6) the 2-skeleton of the (k-1)-simplex is a union of highly symmetric tori and M\"obius strips.

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