Rhombic hectotriadiohedron

Polyhedron composed of 132 rhombic faces
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 (PDF), Research of pattern formation, archived from the original (PDF) on 2016-11-25
  2. ^ "Zonohedrification".
  3. ^ "Zonohedra --- List".
  • 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
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