Supplemental material to the article "Partitions of the triangles of the cross polytope into surfaces''

Details Supplemental material to the article "Partitions of the triangles of the cross polytope into surfaces'' Supplemental material to the article "Partitions of the triangles of the cross polytope into surfaces''

2010-09-14

arxiv.org/abs/1009.2640v1

Mathematics

Combinatorics

459 pages

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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