Great hexacosihecatonicosidishecatonicosachoron

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Great hexacosihecatonicosidishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymGixhidy
Coxeter diagramx3o3o5x5/3*a ()
Elements
Cells600 tetrahedra, 120 dodecahedra, 120 quasitruncated great stellated dodecahedra, 120 quasitruncated small stellated dodecahedra
Faces2400 triangles, 1440 pentagons, 1440 decagrams
Edges3600+3600
Vertices2400
Vertex figureTriangular antipodium, edge lengths 1 (small base), (1+5)/2 (large base), and (5–5)/2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesDoe–5–quit sissid: 144°
 Quit sissid–10/3–quit gissid: 108°
 Tet–3–quit gissid:
Number of external pieces8760
Level of complexity43
Related polytopes
ArmySemi-uniform Sidpixhi, edge lengths (dodecahedra), (tetrahedra)
RegimentGixhidy
ConjugateSmall hexacosihecatonicosidishecatonicosachoron
Abstract & topological properties
Flag count115200
Euler characteristic–480
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The great hexacosihecatonicosidishecatonicosachoron, or gixhidy, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 regular dodecahedra, 120 quasitruncated great stellated dodecahedra, and 120 quasitruncated small stellated dodecahedra. 1 tetrahedron, 1 dodecahedron, 3 quasitruncated great stellated dodecahedra, and 3 quasitruncated small stellated dodecahedra join at each vertex.

Gallery[edit | edit source]

Vertex coordinates[edit | edit source]

The vertices of a great hexacosihecatonicosidishecatonicosachoron of edge length 1 are all permutations of:

along with the even permutations of:

Related polychora[edit | edit source]

The great hexacosihecatonicosidishecatonicosachoron is the colonel of a regiment of 7 members. Its other members include the great hecatonicosafaceted hecatonicosihexacosihecatonicosachoron, great hexacosifaceted trishecatonicosachoron, great hecatonicosihecatonicosihexacosichoron, hecatonicosidishecatonicosachoron, great spinohexacosidishecatonicosachoron, and great spinohecatonicosidishecatonicosachoron.

External links[edit | edit source]