I think by "pierce each other", Jim means that P pierces Q *and* Q pierces P. Andy On Mon, Apr 25, 2016 at 2:05 PM, Veit Elser <ve10@cornell.edu> wrote:
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.
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