# Truncated grand hexacosichoron

Truncated grand hexacosichoron Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymTaggix
Coxeter diagramo5/2o3x3x (         )
Elements
Cells600 truncated tetrahedra, 120 great icosahedra
Faces2400 triangles, 1200 hexagons
Edges720+3600
Vertices1440
Vertex figurePentagrammic pyramid, edge lengths 1 (base) and 3 (sides)
Measures (edge length 1)
Circumradius$\sqrt{\frac{23-9\sqrt5}{2}} \approx 1.19904$ Hypervolume$25\frac{80\sqrt5-161}{4} \approx 111.78399$ Dichoral anglesGike–3–tut: $\arccos\left(-\frac{\sqrt{7-3\sqrt5}}{4}\right) \approx 97.76124^\circ$ Tut–6–tut: $\arccos\left(\frac{3\sqrt5-1}{8}\right) \approx 44.47751^\circ$ Central density191
Number of external pieces80760
Level of complexity269
Related polytopes
ArmySemi-uniform Tex
RegimentTigfix
ConjugateTruncated hexacosichoron
Convex coreHexacosichoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The truncated grand hexacosichoron, or taggix, is a nonconvex uniform polychoron that consists of 120 great icosahedra and 600 truncated tetrahedra. 1 great icosahedron and five truncated tetrahedra join at each vertex. As the name suggests, it can be obtained by truncating the grand hexacosichoron.

## Vertex coordinates

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