Pentitruncated 6-cube

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Pentitruncated 6-cube
Rank6
TypeUniform
Notation
Bowers style acronymTacog
Coxeter diagramx4x3o3o3o3x ()
Elements
Peta192 pentachoric prisms
64 stericated 5-simplices
240 octagonal-tetrahedral duoprisms
60 truncated tesseractic prisms
160 triangular-truncated cubic duoprisms
12 truncated 5-cubes
Tera384+384 pentachora
960+960+960 tetrahedral prisms
1280 triangular duoprisms
960 triangular-octagonal duoprisms
480 truncated cubic prisms
120 truncated tesseracts
Cells1920+1920 tetrahedra
1920+3840+3840 triangular prisms
1440 octagonal prisms
480 truncated cubes
Faces3840+3840 triangles, 1920+5760 squares, 960 octagons
Edges960+3840+3840
Vertices1920
Vertex figureSkew tetrahedral antiprismatic pyramid, edge lengths 1 (base tetrahedra), 2 (sides of antiprism and lacings to one base), and 2+2 (lacings to other base)
Measures (edge length 1)
Circumradius
Hypervolume
Dipetal anglesScad–pen–penp:
 Penp–tepe–otet:
 Otet–todip–tratic: 150°
 Scad–tepe–otet:
 Tattip–ticcup–tratic:
 Scad–triddip–tratic 135°
 Tan–tat–tattip: 135°
 Scad–tepe–tattip:
Central density1
Number of external pieces728
Level of complexity96
Related polytopes
ArmyTacog
RegimentTacog
ConjugateQuasitericellated hexacontatetrapeton
Abstract & topological properties
Flag count4423680
Euler characteristic0
OrientableYes
Properties
SymmetryB6, order 46080
ConvexYes
NatureTame

The pentitruncated 6-cube, also called the pentitruncated dodecapeton, tericellated hexacontatetrapeton, or tacog, is a convex uniform 6-polytope. It consists of 12 truncated 5-cubes, 64 stericated 5-simplices, 192 pentachoric prisms, 60 truncated tesseractic prisms, 240 octagonal-tetrahedral duoprisms, and 160 triangular-truncated cubic duoprisms. 1 truncated 5-cube, 1 stericated 5-simplex, 1 pentachoric prism, 4 truncated tesseractic prisms, 4 octagonal-tetrahedral duoprisms, and 6 triangular-truncated cubic duoprisms join at each vertex. As the name suggests, it is the pentitruncation of the 6-cube.

Vertex coordinates[edit | edit source]

The coordinates of a pentitruncated 6-cube, centered at the origin and with unit edge length, are given by all permutations of:

  • .

Gallery[edit | edit source]

Related polytopes[edit | edit source]

The regiment of the pentitruncated 6-cube contains 15 uniform members.

External links[edit | edit source]