Type: Article

Cleaved abstract polytopes

Pellicer, Daniel;

Abstract:

From a given abstract n-polytope P and a given integer k we derive two abstract polytopes Clk(P) and Cl˜k(P) of ranks n and n?1, respectively. These constructions generalise the truncation of convex polyhedra and the dual of a geometric construction yielding Petrie’s polyhedron {4,6|4}. We determine sufficient and necessary conditions to guarantee that Clk(P) and Cl˜k(P) are regular.