On a generalization of Schönhardt's polyhedron

Jörg Rambau

We show that the non-convex twisted prism over an $n$-gon cannot be triangulated without new vertices. For this, it does not matter what the coordinates of the $n$-gon are as long as the top and the bottom $n$-gon are congruent and the twist is not too large. This generalizes Schönhardt's polyhedron, which is the non-convex twisted prism over a triangle.