Trigonal trapezohedron is one of two special case of the "trigonal trapezohedron" with golden rhombus faces. The "acute" or "prolate" form has three acute angles corners of the rhombic faces meeting at two polar axis vertices. The "obtuse" or "oblate" or "flat" form has three obtuse angle corners of the rhombic faces meeting at the two polar axis vertices. The rhombic hexecontahedron can be constructed by 20 "acute golden rhombohedra" meeting at a point. A regular octahedron augumented by 2 regular tetrahedra creates a "trigonal trapezohedron", with coplanar equilateral triangles merged into 60-degree rhombic faces. Trigonal trapezohedron In geometry, a trigonal trapezohedron
Great rhombihexahedron vertices, and 48 edges. It has 12 outer vertices which have the same vertex arrangement as the cuboctahedron, and 6 inner vertices with the vertex arrangement of an octahedron. As a surface geometry, it can be seen as visually similar to a Catalan solid, the disdyakis dodecahedron, with much taller rhombus-based pyramids joined to each face of a rhombic dodecahedron. Great rhombihexahedron In geometry, the great rhombihexahedron is a nonconvex uniform polyhedron, indexed as U. Its dual is the great rhombihexacron. Its vertex figure is a crossed quadrilateral. There is some controversy on how to colour the faces of this