Great hexacosihecatonicosihecatonicosachoron

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Great hexacosihecatonicosihecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymGixhihy
Coxeter diagramo3o3x5/3x5/2*b ()
Elements
Cells600 tetrahedra, 120 great stellated dodecahedra, 120 great dodecicosidodecahedra
Faces2400 triangles, 1440 pentagrams, 720 decagrams
Edges3600+3600
Vertices2400
Vertex figureTriangular frustum, edge lengths 1 (large base), (5–1)/2 (small base), and (5–5)/2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesGaddid–10/3–gaddid: 108°
 Gaddid–3–tet:
 Gaddid–5/2–gissid: 72°
Number of external pieces18000
Level of complexity75
Related polytopes
ArmySidpixhi, edge length
RegimentGixhihy
ConjugateSmall hexacosihecatonicosihecatonicosachoron
Abstract & topological properties
Flag count86400
Euler characteristic–1080
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

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

Vertex coordinates[edit | edit source]

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

along with the even permutations of:

Related polychora[edit | edit source]

The great hexacosihecatonicosihecatonicosachoron is the colonel of a regiment of 7 members. Its other members include the quasidisprismatohexacosihecatonicosachoron, diprismatohecatonicosachoron, great hecatonicosafaceted prismatohecatonicosihexacosichoron, great hexacosifaceted prismatodishecatonicosachoron, great spinoprismatohexacosihecatonicosachoron, and great spinoprismatodishecatonicosachoron.

External links[edit | edit source]