Omnitruncated 5-cube

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Omnitruncated 5-cube
Rank5
TypeUniform
Notation
Bowers style acronymGacnet
Coxeter diagramx4x3x3x3x ()
Elements
Tera80 hexagonal-octagonal duoprisms, 80 truncated octahedral prisms, 40 great rhombicuboctahedral prisms, 32 great prismatodecachora, 10 great disprismatotesseractihexadecachora
Cells480 cubes, 320+320+320+320 hexagonal prisms, 240+240 octagonal prisms, 160+160 truncated octahedra, 80 great rhombicuboctahedra
Faces960+960+960+960+960+960 squares, 640+640+640 hexagons, 480 octagons
Edges1920+1920+1920+1920+1920
Vertices3840
Vertex figureIrregular pentachoron, edge lengths 2 (6), 3 (3), and 2+2 (1)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesGippid–toe–tope:
 Tope–hip–hodip: 150°
 Gircope–op–hodip:
 Gippid–hip–hodip:
 Gircope–cube–tope: 135°
 Gidpith–girco–gircope: 135°
 Gippid–hip–gircope:
 Gidpith–op–hodip:
 Gidpith–hip–tope: 120°
 Gidpith–toe–gippid:
Central density1
Number of external pieces242
Level of complexity120
Related polytopes
ArmyGacnet
RegimentGacnet
DualPentachoric trischilliaoctacositetracontateron
ConjugateGreat quasicellipenteractitriacontaditeron
Abstract & topological properties
Flag count460800
Euler characteristic2
OrientableYes
Properties
SymmetryB5, order 3840
ConvexYes
NatureTame

The omnitruncated 5-cube, also called the great cellated penteractitriacontaditeron, great cellipenteractitriacontaditeron, or gacnet, is a convex uniform 5-polytope. It consists of 80 hexagonal-octagonal duoprisms, 80 truncated octahedral prisms, 40 great rhombicuboctahedral prisms, 32 great prismatodecachora, and 10 great disprismatotesseractihexadecachora. One of each type of facet joins at each vertex. As the name suggests, it is the omnitruncate of the B5 family.

This polyteron can be alternated into a snub penteract, although it cannot be made uniform.

Vertex coordinates[edit | edit source]

The vertices of an omnitruncated 5-cube of edge length 1 are given by all permutations of:

  • .

Gallery[edit | edit source]

External links[edit | edit source]