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
Regular dodecahedron of a regular dodecahedron centered at the origin and suitably scaled and oriented: where is the golden ratio (also written "τ") ≈ 1.618. The edge length is . The circumradius is . Similar to the symmetry of the vertex coordinates, the equations of the twelve facets of the regular dodecahedron also display symmetry in their coefficients: The "regular dodecahedron" is the third in an infinite set of truncated trapezohedra which can be constructed by truncating the two axial vertices of a pentagonal trapezohedron. The stellations of the regular dodecahedron make up three of the four Kepler–Poinsot polyhedra. A rectified regular