Triangular gyroprism

The triangular gyroprism, or trigyp, is a triangle-based gyroprism, a variant of the triangular antiprism where the bases are rotated by an angle other than 60°, and has 6 scalene triangles for its sides instead of isosceles triangles. It can be formed by alternating a ditrigonal prism.

The triangular gyroprism is topologically equivalent to the nonconvex Schönhardt polyhedron, the simplest non-convex polyhedron that cannot be triangulated into tetrahedra, meaning that there is no vertex-inscribed tetrahedron that lies entirely inside the Schönhardt polyhedron.