A new Petrie-like construction for abstract polytopes

摘要

This article introduces a new construction for polytopes, that may be seen as a generalisation of the Petrie dual to higher ranks. Some theoretical results are derived regarding when the construction can be expected to work, and the construction is applied to some special cases. In particular, the generalised Petrie duals of the hypercubes are enumerated. (C) 2008 Elsevier Inc. All rights reserved.