High Quality Content by WIKIPEDIA articles! In geometry, the Schonhardt polyhedron is the smallest non-convex polyhedron that cannot be triangulated into tetrahedra without adding new vertices. It is named after German mathematician Erich Schonhardt, who first described it in 1928.The Schonhardt polyhedron can be formed by two congruent equilateral triangles in two parallel planes, such that the line through the centers of the triangles is perpendicular to the planes. The two triangles should be twisted with respect to each other, so that they are neither translates of each other nor 180-degree reflections of each other.

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