Rectified hecatonicosachoron

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Rectified hecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymRahi
Coxeter diagramo5x3o3o ()
Elements
Cells600 tetrahedra, 120 icosidodecahedra
Faces2400 triangles, 720 pentagons
Edges3600
Vertices1200
Vertex figureSemi-uniform triangular prism, edge lengths 1 (base) and (1+5)/2 (side)
Edge figuretet 3 id 5 id 3
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesId–3–tet:
 Id–5–id: 144°
Central density1
Number of external pieces720
Level of complexity3
Related polytopes
ArmyRahi
RegimentRahi
DualJoined hexacosichoron
ConjugateRectified great grand stellated hecatonicosachoron
Abstract & topological properties
Flag count43200
Euler characteristic0
OrientableYes
Properties
SymmetryH4, order 14400
ConvexYes
NatureTame

The rectified hecatonicosachoron, or rahi, also commonly called the rectified 120-cell, is a convex uniform polychoron that consists of 600 regular tetrahedra and 120 icosidodecahedra. Two tetrahedra and three icosidodecahedra join at each triangular prismatic vertex. As the name suggests, it can be obtained by rectifying the hecatonicosachoron.

Cross-sections[edit | edit source]

Vertex coordinates[edit | edit source]

The vertices of a rectified hecatonicosachoron of edge length 1 are given by all permutations of:

  • ,
  • ,
  • ,
  • ,

along with all even permutations of:

  • ,
  • ,
  • ,
  • ,
  • ,
  • .

Representations[edit | edit source]

A rectified hecatonicosachoron has the following Coxeter diagrams:

  • o5x3o3o (full symmetry)
  • ofxoxooxFf(oV)fFxooxoxfo5xoxfofFxoo(xo)ooxFfofxox3oooxFfofxF(Vo)FxfofFxooo&#xt (H3 axial, icosidodecahedron-first)

Related polychora[edit | edit source]

The rectified hecatonicosachoron is the colonel of a 3-member regiment that also includes the facetorectified hecatonicosachoron and small hecatonicosintercepted hecatonicosachoron.

Isogonal derivatives[edit | edit source]

Substitution by vertices of these following elements will produce these convex isogonal polychora:

External links[edit | edit source]