Rectified great stellated hecatonicosachoron

From Polytope Wiki
Jump to navigation Jump to search
Rectified great stellated hecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymRagishi
Coxeter diagramo5/2x3o5o ()
Elements
Cells
Faces
Edges3600
Vertices720
Vertex figureSemi-uniform Pentagonal prism, edge lengths 1 (base) and (5–1)/2 (side)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angleGid–5/2–gid: 144°
Ike–3–gid: 120°
Central density20
Number of external pieces5160
Level of complexity20
Related polytopes
ArmyRox, edge length
RegimentRagishi
ConjugateRectified grand hecatonicosachoron
Convex coreHecatonicosachoron
Abstract & topological properties
Flag count43200
Euler characteristic0
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The rectified great stellated hecatonicosachoron, or ragishi, is a nonconvex uniform polychoron that consists of 120 icosahedra and 120 great icosidodecahedra. Two icosahedra and five great icosidodecahedra join at each pentagonal prismatic vertex. As the name suggests, it can be obtained by rectifying the great stellated hecatonicosachoron.

Gallery[edit | edit source]

Card with cell counts, vertex figure, and cross-sections.

Vertex coordinates[edit | edit source]

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

  • ,
  • ,

along with even permutations of:

  • ,
  • ,
  • ,
  • .

Related polychora[edit | edit source]

The rectified great stellated hecatonicosachoron is the colonel of a regiment with 15 members. Of these, one other besides the colonel itself is Wythoffian (the rectified grand stellated hecatonicosachoron), two are hemi-Wythoffian (the small pentagrammal antiprismatoverted dishecatonicosachoron and pentagonal retroprismatoverted hexacosihecatonicosachoron), and one is noble (the great retropental hecatonicosachoron).

It has the same circumradius as the hexagonal-decagrammic duoprism.

Uniform polychoron compounds composed of rectified great stellated hecatonicosachora include:

External links[edit | edit source]