Great ditrigonal hecatonicosihexacosihecatonicosachoron

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Great ditrigonal hecatonicosihexacosihecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymGidthixhi
Coxeter diagramo3o3x5/3x5*b ()
Elements
Cells600 tetrahedra, 120 dodecahedra, 120 great ditrigonal dodecicosidodecahedra
Faces2400 triangles, 1440 pentagons, 720 decagrams
Edges3600+3600
Vertices2400
Vertex figureTriangular frustum, edge lengths 1 (small base), (1+5)/2 (large base), and (5–5)/2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesGidditdid–3–tet:
 Gidditdid–10/3–gidditdid: 144°
 Gidditdid–5–doe: 144°
Number of external pieces5520
Level of complexity30
Related polytopes
ArmyThi, edge length
RegimentGidthixhi
ConjugateSmall ditrigonal hecatonicosihexacosihecatonicosachoron
Abstract & topological properties
Flag count86400
Euler characteristic–1080
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

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

Gallery[edit | edit source]

Card with cell counts, vertex figure, and cross-sections.


Vertex coordinates[edit | edit source]

The vertices of a great ditrigonal hecatonicosihexacosihecatonicosachoron of edge length 1 are given by all permutations of:

along with all even permutations of:

Related polychora[edit | edit source]

The great ditrigonal hecatonicosihexacosihecatonicosachoron is the colonel of a regiment of 7 members. Its other members include the great dishexacosidishecatonicosachoron, hexacosihecatonicosintercepted hecatonicosachoron, great hecatonicosafaceted hexacosidishecatonicosachoron, great hexacosifaceted hexacosidishecatonicosachoron, great spinotrishecatonicosachoron, and great spinohecatonicosidishexacosichoron.

External links[edit | edit source]