Rhombic hectotriadiohedron
| Rhombic hectotriadiohedron | |
|---|---|
Two different types: Type T and Type C, respectively | |
| Type | zonohedron |
| Faces | 132 rhombi |
| Edges | 264 |
| Vertices | 134 |
| Symmetry group | octahedral symmetry |
| Properties | convex |
In geometry, a rhombic hectotriadiohedron, rhombhectotriadiohedron,[1] rhombic 132-hedron, or equilateral dodecazonohedron[2] is a polyhedron composed of 132 rhombic faces. Rhombic faces have five positions within octahedral symmetry.[2] There are two topological types, with the same number of elements and the same symmetry but with a somewhat different arrangement of rhombic faces.[1]
There are two types of rhombic hectotridiohedron: the type T and C. The type T has eight rhombi meeting at the center of a cube's six faces. The three meet at the 8 corners of a cube. The twelve are positioned along the twelve edges of a cube, and four more surround each of the twelve edges of a cube. This polyhedron is a 12-zone zonohedrification[3] of the rhombicuboctahedron.[4] The type C is a 12-zone zonohedrification of a truncated cube.
See also
- Trigonal trapezohedron - 6 rhombi
- Rhombic dodecahedron - 12 rhombi
- Rhombic icosahedron - 20 rhombi
- Rhombic triacontahedron - 30 rhombi
- Rhombic hexecontahedron - 60 rhombi
- Rhombic enneacontahedron - 90 rhombi
References
- ^ a b Watanabe, Y.; Betsumiya, T., Derivation of Some Equilateral Zonohedra and Star Zonohedra (PDF), Research of pattern formation, archived from the original (PDF) on 2016-11-25.
- ^ a b Hanegraaf, Anton (1980), Twenty Questions on Zonogons, Zonohedra and Zonoids (PDF), Université du Quebéc à Montréal, pp. 31–40.
- ^ "Zonohedrification".
- ^ "Zonohedra --- List".
- George Hart
- zono-12 from rhombicubocahedron Archived 2023-03-06 at the Wayback Machine VRML model
- zono-12 from truncated cube Archived 2023-03-06 at the Wayback Machine VRML model
- Rhombic Polyhedron with 132 Faces
- rhombic 132-hedron within a cube