Abstract: The main purpose of this paper is to popularize Danzer’s power complex construction and establish some new results about covering maps between two power complexes. Power complexes are cube-like combinatorial structures that share many structural properties with higher-dimensional cubes and cubical tessellations on manifolds. Power complexes that are also abstract polytopes have repeatedly appeared somewhat unexpectedly in various contexts, although often under a different name. However, the non-polytope case is largely unexplored.

Keywords: cube; cubical tessellation; abstract polytope; incidence complex; covering.

MSC (2000): Primary: 51M20. Secondary: 52B15.

Link:

CUBE-LIKE POLYTOPES AND COMPLEXES

Andrew Duke, Egon Schulte

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p05.pdf