Great disprismatohexacosihecatonicosachoron

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Great disprismatohexacosi-hecatonicosachoron
Omnitruncated 120-cell wireframe.png
Bowers style acronymGidpixhi
Coxeter diagramx5x3x3x (CDel node 1.pngCDel 5.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png)
Cells1200 hexagonal prisms, 720 decagonal prisms, 600 truncated octahedra, 120 great rhombicosidodecahedra
Faces3600+3600+3600 squares, 2400+2400 hexagons, 1440 decagons
Vertex figureIrregular tetrahedron, edge lengths 2 (3), 3 (2), and (5+5)/2 (1)
Measures (edge length 1)
Dichoral anglesToe–6–hip:
 Grid–10–dip: 162°
Central density1
Number of external pieces2640
Level of complexity24
Related polytopes
DualTetrahedral myriatetrachiliatetracosichoron
ConjugateGreat quasidisprismatohexacosihecatonicosachoron
Abstract & topological properties
Flag count345600
Euler characteristic0
SymmetryH4, order 14400

The great disprismatohexacosihecatonicosachoron, or gidpixhi, also commonly called the omnitruncated 120-cell, is a convex uniform polychoron that consists of 1200 hexagonal prisms, 720 decagonal prisms, 600 truncated octahedra, and 120 great rhombicosidodecahedra. 1 of each type of cell join at each vertex. It is the omnitruncate of the H4 family of uniform polychora, and could also be considered to be the omnitruncated 600-cell. It is therefore the most complex of the non-prismatic convex uniform polychora.

This polychoron can be alternated into a snub hexacosihecatonicosachoron, although it cannot be made uniform.

Cross-sections[edit | edit source]

Gidpixhi sections Bowers.png Gidpixhi-slices.gif

Vertex coordinates[edit | edit source]

Vertex coordinates for a great disprismatohexacosihecatonicosachoron of edge length 1 are given by all permutations of:

plus all even permutations of:

Semi-uniform variant[edit | edit source]

The great disprismatohexacosihecatonicosachoron has a semi-uniform variant of the form a5b3c3d that maintains its full symmetry. This variant uses 120 great rhombicosidodecahedra of form a5b3c, 600 great rhombitetratetrahedra of form b3c3d, 720 dipentagonal prisms of form d a5b, and 1200 ditrigonal prisms of form a c3d as cells, with 4 edge lengths.

With edges of length a, b, c, and d (such that it forms a5b3c3d), its circumradius is given by .

Related polychora[edit | edit source]

o5o3o3o truncations
Name OBSA CD diagram Picture
Hecatonicosachoron hi x5o3o3o
Schlegel wireframe 120-cell.png
Truncated hecatonicosachoron thi x5x3o3o
Schlegel half-solid truncated 120-cell.png
Rectified hecatonicosachoron rahi o5x3o3o
Hexacosihecatonicosachoron xhi o5x3x3o
Rectified hexacosichoron rox o5o3x3o
Rectified 600-cell schlegel halfsolid.png
Truncated hexacosichoron tex o5o3x3x
Schlegel half-solid truncated 600-cell.png
Hexacosichoron ex o5o3o3x
Schlegel wireframe 600-cell.png
Small rhombated hecatonicosachoron srahi x5o3x3o
Great rhombated hecatonicosachoron grahi x5x3x3o
Cantitruncated 120-cell.png
Small rhombated hexacosichoron srix o5x3o3x
Great rhombated hexacosichoron grix o5x3x3x
Cantitruncated 600-cell.png
Small disprismatohexacosihecatonicosachoron sidpixhi x5o3o3x
Runcinated 120-cell.png
Prismatorhombated hexacosichoron prix x5x3o3x
Runcitruncated 120-cell.png
Prismatorhombated hecatonicosachoron prahi x5o3x3x
Runcitruncated 600-cell.png
Great disprismatohexacosihecatonicosachoron gidpixhi x5x3x3x
Omnitruncated 120-cell wireframe.png

External links[edit | edit source]