Supplemental material to the article "Partitions of the triangles of the cross polytope into surfaces''
Abstract
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 Möbius strips.
SSupplemental material to the article “Partitions of thetriangles of the cross polytope into surfaces”
Jonathan Spreer
Abstract
We present a constructive proof, that there exists a decomposition of the -skeleton of the k -dimensional cross polytope β k into closed surfaces of genus ⁄ , each with a transitiveautomorphism group given by the vertex transitive Z k -action on β k . Furthermore weshow, that for each k (cid:17) , p q the -skeleton of the p k (cid:1) q -simplex is a union of highlysymmetric tori and Möbius strips. MSC 2010: 52B12 ; 52B70; 57Q15; 57M20; 05C10;