From:mmcconn@math.okstate.edu (Mark McConnell)Newsgroups:sci.math.researchSubject:Re: embeddings of cubeDate:Wed, 17 Nov 1993 06:45:03 GMTOrganization:/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.