From: email@example.com (Mark McConnell) Newsgroups: sci.math.research Subject: Re: embeddings of cube Date: Wed, 17 Nov 1993 06:45:03 GMT Organization: /etc/organization
I can't resist posting a related problem. By a hexahedron we mean any convex polyhedron in R^3 combinatorially equivalent to a cube; that is, a polyhedron with six quadrilateral faces meeting three at each corner. Assume that three of the four body diagonals meet at a common point. Prove that all four of the body diagonals meet at a common point. This has applications to how many projective toric varieties can have a (combinatorial equivalent of the) octahedron as their image under the moment map.