# Truncated grand hecatonicosachoron

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Truncated grand hecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymTaghi
Coxeter diagramo5/2o3x5x ()
Elements
Cells120 great icosahedra, 120 truncated dodecahedra
Faces2400 triangles, 720 decagons
Edges720+3600
Vertices1440
Vertex figurePentagrammic pyramid, edge lengths 1 (base) and (5+5)/2 (side)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {13+5{\sqrt {5}}}{2}}}\approx 3.47709}$
Hypervolume${\displaystyle 50\left(46+21{\sqrt {5}}\right)\approx 4647.87138}$
Dichoral anglesGike–3–tid: 120°
Tid–10–tid: 72°
Central density20
Number of external pieces21720
Level of complexity71
Related polytopes
ArmySemi-uniform Tex, edge lengths ${\displaystyle {\frac {{\sqrt {5}}-1}{2}}}$ (icosahedra), 1 (surrounded by truncated tetrahedra)
RegimentTighi
ConjugateQuasitruncated great stellated hecatonicosachoron
Convex coreHecatonicosachoron
Abstract & topological properties
Flag count57600
Euler characteristic0
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The truncated grand hecatonicosachoron, or taghi, is a nonconvex uniform polychoron that consists of 120 great icosahedra and 120 truncated dodecahedra. One great icosahedron and five truncated dodecahedra join at each vertex. As the name suggests, it can be obtained by truncating the grand hecatonicosachoron.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the truncated great hecatonicosachoron.