Mark Broadie

A theorem about antiprisms

Let P be a polytope in Rn containing the origin in its interior, and let P* be the algebraic dual polytope of P. Let Q Rn x [0,1] be the (n+1)-dimensional polytope that is the convex hull of P x {1} and P* x {0}. For each face F of P, let Q(F) denote the convex hull of F x {1} and F* x {0}, where F* is the dual face of P*. Then Q is an antiprism if the set of facets of Q is precisely the collection {Q (F)} for all faces F of P. If Q is an antiprism, the correspondence between primal and dual faces of P and P* is manifested in the facets of Q. In this paper, necessary and sufficient conditions for the existence of antiprisms are stated and proved.

Source: Linear Algebra and Its Applications
Exact Citation:
Broadie, Mark. "A theorem about antiprisms." Linear Algebra and Its Applications 66 (April 1985): 99-111.
Volume: 66
Pages: 99-111
Date: 4 1985