Talk:Opposite vertices of base polyhedra
From Egres Open
An example -- Tamás Király 22:52, 24 November 2009 (UTC)
Base polyhedra are exactly the polyhedra that have edge vectors of the form [math]x_i-x_j[/math]. It is easy to see that the conjecture is not true for the more general class of polyhedra with edge vectors of the form [math]x_i-x_j[/math] and [math]x_i+x_j[/math]. For example, the tetrahedron with vertices (1,-1,-1), (-1,1,-1), (-1,-1,1), (1,1,1) has 0 in the interior but it has no opposite vertices.
