Rhombic hectotriadiohedron

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

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]

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

1. Y. Watanabe, T. Betsumiya Derivation of Some Equilateral Zonohedra and Star Zonohedra, Research of pattern formation
2. http://www.georgehart.com/virtual-polyhedra/zonohedrification.html
3. 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