# Great dishexacosidishecatonicosachoron

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Great dishexacosidishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymGadixady
Coxeter diagramx3x3/2o3o5*a ()
Elements
Cells600 tetrahedra, 120 dodecahedra, 600 truncated tetrahedra, 120 truncated icosahedra
Faces2400 triangles, 1440 pentagons, 2400 hexagons
Edges3600+3600
Vertices2400
Vertex figureTriangular retroantipodium, edge lengths 1 (small base), (1+5)/2 (large base), and 3 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {13+3{\sqrt {5}}}{2}}}\approx 3.13912}$
Hypervolume${\displaystyle 5{\frac {365+322{\sqrt {5}}}{2}}\approx 2712.53471}$
Dichoral anglesDoe–5–ti: 72°
Tet–3–tut: ${\displaystyle \arccos \left({\frac {3{\sqrt {5}}-1}{8}}\right)\approx 44.47751^{\circ }}$
Ti–6–tut: ${\displaystyle \arccos \left({\frac {\sqrt {10}}{4}}\right)\approx 37.37737^{\circ }}$
Number of external pieces909840
Level of complexity1984
Related polytopes
ArmyThi, edge length ${\displaystyle {\frac {3-{\sqrt {5}}}{2}}}$
RegimentGidthixhi
ConjugateSmall dishexacosidishecatonicosachoron
Abstract & topological properties
Flag count115200
Euler characteristic0
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The great dishexacosidishecatonicosachoron, or gadixady, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 regular dodecahedra, 600 truncated tetrahedra, and 120 truncated icosahedra. 1 tetrahedron, 1 dodecahedron, 3 truncated tetrahedra, and 3 truncated icosahedra join at each vertex.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the great ditrigonal hecatonicosihexacosihecatonicosachoron.