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
Bilinski dodecahedron of lengths of the two diagonals is the golden ratio; that is, the faces of this shape are golden rhombi. In contrast, for the standard rhombic dodecahedron the corresponding ratio is the square root of 2. This shape is a zonohedron. Like the rhombic dodecahedron, it can tile three-dimensional space by translation, making it a parallelohedron. The Bilinski dodecahedron and rhombic dodecahedron have the same topology: their vertices, edges, and faces correspond one-for-one, in an adjacency-preserving way. However, their geometry is different. In a 1962 paper, H. S. M. Coxeter claimed that the Bilinski dodecahedron could be obtained by an