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We present a constructive proof, that there exists a decomposition of the2-skeleton of the k-dimensional cross polytope \beta^k into closed surfaces ofgenus \leq 1, each with a transitive automorphism group given by the vertextransitive 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 highlysymmetric tori and M\"obius strips.

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