# Rectified great grand stellated hecatonicosachoron

Rectified great grand stellated hecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymRigogishi
Coxeter diagramo5/2x3o3o ()
Elements
Cells
Faces
Edges3600
Vertices1200
Vertex figureSemi-uniform triangular prism, edge lengths 1 (base) and (5–1)/2 (side)
Edge figuretet 3 gid 5/2 gid 3
Measures (edge length 1)
Circumradius${\displaystyle {\frac {3{\sqrt {3}}-{\sqrt {15}}}{2}}\approx 0.66158}$
Hypervolume${\displaystyle 5{\frac {331{\sqrt {5}}-730}{4}}\approx 12.67313}$
Dichoral anglesGid–3–tet: ${\displaystyle \arccos \left(-{\frac {\sqrt {7-3{\sqrt {5}}}}{4}}\right)\approx 97.76124^{\circ }}$
Gid–5/2–gid: 72°
Central density191
Number of external pieces27600
Level of complexity71
Related polytopes
ArmyRahi, edge length ${\displaystyle {\frac {7-3{\sqrt {5}}}{2}}}$
RegimentRigogishi
ConjugateRectified hecatonicosachoron
Convex coreRectified hecatonicosachoron
Abstract & topological properties
Flag count43200
Euler characteristic0
OrientableYes
Properties
SymmetryH4, order 14400
Flag orbits3
ConvexNo
NatureTame

The rectified great grand stellated hecatonicosachoron, or rigogishi, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra and 120 great icosidodecahedra. Two tetrahedra and three great icosidodecahedra join at each triangular prismatic vertex. As the name suggests, it can be obtained by rectifying the great grand stellated hecatonicosachoron.

## Vertex coordinates

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

• ${\displaystyle \left(0,\,0,\,\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm \left({\sqrt {5}}-2\right)\right)}$,
• ${\displaystyle \left(0,\,\pm {\frac {3-{\sqrt {5}}}{2}},\,\pm {\frac {3-{\sqrt {5}}}{2}},\,\pm {\frac {3-{\sqrt {5}}}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm 3{\frac {3-{\sqrt {5}}}{4}}\right)}$,
• ${\displaystyle \left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {3{\sqrt {5}}-5}{4}},\,\pm {\frac {3{\sqrt {5}}-5}{4}}\right)}$,

along with all even permutations of:

• ${\displaystyle \left(0,\,\pm {\frac {1}{2}},\,\pm {\frac {7-3{\sqrt {5}}}{4}},\,\pm {\frac {3{\sqrt {5}}-5}{4}}\right)}$,
• ${\displaystyle \left(0,\,\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm 3{\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {{\sqrt {5}}-2}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm \left({\sqrt {5}}-2\right),\,\pm {\frac {3-{\sqrt {5}}}{4}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {7-3{\sqrt {5}}}{4}},\,\pm {\frac {3-{\sqrt {5}}}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {3{\sqrt {5}}-5}{4}},\,\pm {\frac {3-{\sqrt {5}}}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {7-3{\sqrt {5}}}{4}},\,\pm {\frac {{\sqrt {5}}-2}{2}}\right)}$.

## Related polychora

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