From:  (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

This has applications to how many projective toric varieties can have
a (combinatorial equivalent of the) octahedron as their image under
the moment map.