Rhombic hectotriadiohedron
| Rhombic hectotriadiohedron | |
|---|---|
| File:130px130px 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][better source needed] The type C is a 12-zone zonohedrification of a truncated cube.[citation needed]
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
- ↑ 1.0 1.1 Watanabe, Y.; Betsumiya, T., Derivation of Some Equilateral Zonohedra and Star Zonohedra, Research of pattern formation, http://www.scipress.org/e-library/rpf/pdf/chap2/0055.PDF.
- ↑ 2.0 2.1 Hanegraaf, Anton (1980), Twenty Questions on Zonogons, Zonohedra and Zonoids, Université du Quebéc à Montréal, pp. 31–40, https://www.iri.upc.edu/people/ros/StructuralTopology/ST4/st4-08-a4-ocr.pdf.
- ↑ "Zonohedrification". http://www.georgehart.com/virtual-polyhedra/zonohedrification.html.
- ↑ "Zonohedra --- List". http://www.georgehart.com/virtual-polyhedra/zonohedra-index.html.
- George Hart
- zono-12 from rhombicubocahedron VRML model
- zono-12 from truncated cube VRML model
- Rhombic Polyhedron with 132 Faces
- rhombic 132-hedron within a cube
 |  |
