Rhombic hectotriadiohedron
In geometry, a rhombic hectotriadiohedron, rhombhectotriadiohedron or rhombic 132-hedron is a polyhedron composed of 132 rhombic faces. Rhombic faces have 5 positions within octahedral symmetry. There are two topological types, with the same number of elements, the same symmetry, but having a somewhat different arrangement of rhombic faces.[1]
| Rhombic hectotriadiohedron | |
|---|---|
  Type T and Type C | |
| Type | zonohedron |
| Face polygon | rhombus |
| Faces | 132 rhombi |
| Edges | 264 |
| Vertices | 134 |
| Symmetry group | Oh, [4,3], *432 |
| Properties | convex, zonohedron |
The type T has 8 rhombi meeting at the center positions of a cube's 6 faces. 3 meet at the 8 corners of a cube. 12 are positioned along the 12 edges of a cube, and 4 more surround each of 12 edges of a cube. It is a 12-zone zonohedrification[2] of the rhombicuboctahedron.[3]
Type C is a 12-zone zonohedrification of a truncated cube.
See also
- Trigonal trapezohedron - 6 rhombi
- Rhombic dodecahedron - 12 rhombi
- Rhombic triacontahedron - 30 rhombi
- Rhombic hexecontahedron - 60 rhombi
- Rhombic enneacontahedron - 90 rhombi
References
- Y. Watanabe, T. Betsumiya Derivation of Some Equilateral Zonohedra and Star Zonohedra, Research of pattern formation
- http://www.georgehart.com/virtual-polyhedra/zonohedrification.html
- http://www.georgehart.com/virtual-polyhedra/zonohedra-index.html
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