25 Apr
2016
25 Apr
'16
12:06 p.m.
On Apr 25, 2016, at 11:36 AM, James Propp <jamespropp@gmail.com> wrote:
Given convex polytopes P and Q in R^n, say P "pierces" Q if Q\P is connected but not simply connected.
Are there convex polyhedra P,Q in R^3 that pierce each other? (I don't think so but no proof leaps to mind.)
How about: Q=convex polyhedron approximation of oblate ellipsoid P=convex polyhedron approximation of prolate ellipsoid If their centers and symmetry axes coincide, and the short(long) diameter of Q is less(greater) than the long(short) diameter of P, then Q\P is a torus. -Veit