On polytopes cut by flats

Abstract

We prove that if we cut a d-polytope by a k-flat, then the complex of the uncut faces has the same simple-homotopy type as the boundary complex of a (d-k)-polytope. We also investigate the combinatorial properties of the complex of the uncut faces and, as a corollary, we answer negatively a question of Goodman and Pach. © 1995 Springer-Verlag New York Inc.