Rectified great grand hecatonicosachoron

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Rectified great grand hecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymRagaghi
Coxeter diagramo5x5/2o3o ()
Elements
Cells
Faces
Edges3600
Vertices1200
Vertex figureSemi-uniform triangular prism, edge lengths (5–1)/2 (base) and (1+5)/2 (side)
Edge figuregissid 5/2 did 5 did 5/2
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesDid–5/2–gissid: 108°
 Did–5–did: 72°
Central density76
Number of external pieces34920
Level of complexity141
Related polytopes
ArmyRahi, edge length
RegimentRagaghi
ConjugateRectified small stellated hecatonicosachoron
Convex coreHecatonicosachoron
Abstract & topological properties
Flag count43200
Euler characteristic–480
OrientableYes
Properties
SymmetryH4, order 14400
Flag orbits3
ConvexNo
NatureTame

The rectified great grand hecatonicosachoron, or ragaghi, is a nonconvex uniform polychoron that consists of 120 great stellated dodecahedra and 120 dodecadodecahedra. Two great stellated dodecahedra and three dodecadodecahedra join at each triangular prismatic vertex. As the name suggests, it can be obtained by rectifying the great grand hecatonicosachoron.

Gallery[edit | edit source]

Vertex coordinates[edit | edit source]

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

  • ,
  • ,
  • ,
  • ,

along with all even permutations of:

  • ,
  • ,
  • ,
  • ,
  • ,
  • .

Related polychora[edit | edit source]

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

External links[edit | edit source]