Abstract
The natural mixing construction for abstract polytopes provides a way to build a minimal common cover of two regular or chiral polytopes. With the help of the chirality group of a polytope, it is often possible to determine when the mix of two chiral polytopes is still chiral. By generalizing the chirality group to a whole family of variance groups, we can explicitly describe the structure of the mix of two polytopes. We are also able to determine when the mix of two polytopes is invariant under other external symmetries, such as duality and Petrie duality.KeywordsAbstract regular polytopeChiral polytopeSelf-dual polytopeChiral mapPetrie dualExternal symmetrySubject ClassificationsPrimary 52B15Secondary: 51M2005C25
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