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 ${\displaystyle \mathrm {O} _{\mathrm {h} }}$
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. 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.
2. Hanegraaf, Anton (1980), Twenty Questions on Zonogons, Zonohedra and Zonoids (PDF), Université du Quebéc à Montréal, pp. 31–40.
3. "Zonohedrification".
4. "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