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 faces) is while the midradius, which touches the middle of each edge, is These quantities may also be expressed as where "ϕ" is the golden ratio. Note that, given a regular dodecahedron of edge length one, "r" is the radius of a circumscribing sphere about a cube of edge length "ϕ", and "r" is the apothem of a regular pentagon of edge length "ϕ". The surface area "A" and the volume "V" of a regular dodecahedron of edge length "a" are: Additionally, the surface area and volume of a regular dodecahedron are related to the golden ratio. A dodecahedron with