# Truncated grand hexacosichoron

Truncated grand hexacosichoron
Rank4
TypeUniform
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${\displaystyle {\sqrt {\frac {23-9{\sqrt {5}}}{2}}}\approx 1.19904}$
Hypervolume${\displaystyle 25{\frac {80{\sqrt {5}}-161}{4}}\approx 111.78399}$
Dichoral anglesGike–3–tut: ${\displaystyle \arccos \left(-{\frac {\sqrt {7-3{\sqrt {5}}}}{4}}\right)\approx 97.76124^{\circ }}$
Tut–6–tut: ${\displaystyle \arccos \left({\frac {3{\sqrt {5}}-1}{8}}\right)\approx 44.47751^{\circ }}$
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.