# Great ditrigonary hexacosihecatonicosachoron

Great ditrigonary hexacosihecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymGidtixhi
Coxeter diagramx3o3o3/2o5*b ()
Elements
Cells600 tetrahedra, 120 icosahedra
Faces2400 triangles
Edges1200
Vertices120
Vertex figureGreat ditrigonary icosidodecahedron, edge length 1
Edge figure(tet 3 ike 3)×3
Measures (edge length 1)
Hypervolume${\displaystyle 25{\frac {1+2{\sqrt {5}}}{4}}\approx 34.20085}$
Dichoral angle${\displaystyle \arccos \left(-{\frac {\sqrt {7-3{\sqrt {5}}}}{4}}\right)\approx 97.76124^{\circ }}$
Central density39
Number of external pieces57600
Level of complexity154
Related polytopes
ArmyEx, edge length ${\displaystyle {\frac {{\sqrt {5}}-1}{2}}}$
RegimentSishi
CompanySidtixhi
DualGreat triambic icosahedral hecatonicosachoron
ConjugateSmall ditrigonary hexacosihecatonicosachoron
Abstract & topological properties
Flag count28800
Euler characteristic600
OrientableYes
Properties
SymmetryH4, order 14400
Flag orbits2
ConvexNo
NatureTame

The great ditrigonary hexacosihecatonicosachoron, or gidtixhi, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra and 120 regular icosahedra. 12 icosahedra and 20 tetrahedra join at each vertex, with a great ditrigonary icosidodecahedron as the vertex figure.

It has the same set of triangular faces as the small ditrigonary hexacosihecatonicosachoron.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small stellated hecatonicosachoron.