Great ditrigonal hecatonicosihexacosihecatonicosachoron

From Polytope Wiki
Jump to navigation Jump to search
Great ditrigonal hecatonicosihexacosihecatonicosachoron
Gidthixhi card Bowers.jpeg
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymGidthixhi
Coxeter diagramo3o3x5/3x5*b (CDel label5-3.pngCDel branch 11.pngCDel split2-53.pngCDel node.pngCDel 3.pngCDel node.png)
Elements
Vertex figureTriangular frustum, edge lengths 1 (small base), (1+5)/2 (large base), and (5–5)/2 (sides)
Cells600 tetrahedra, 120 dodecahedra, 120 great ditrigonal dodecicosidodecahedra
Faces2400 triangles, 1440 pentagons, 720 decagrams
Edges3600+3600
Vertices2400
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesGidditdid–3–tet:
 Gidditdid–10/3–gidditdid: 144°
 Gidditdid–5–doe: 144°
Euler characteristic–1080
Number of pieces5520
Level of complexity30
Related polytopes
ArmyThi
RegimentGidthixhi
ConjugateSmall ditrigonal hecatonicosihexacosihecatonicosachoron
Topological properties
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.

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]