Truncated 2 21 polytope

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Truncated 2 21 polytope
Rank6
TypeUniform
Notation
Bowers style acronymTojak
Coxeter diagramx3x3o3o3o *c3o ()
Elements
Peta27 demipenteracts, 72 truncated hexatera, 27 truncated triacontaditera
Tera432 pentachora, 270 hexadecachora, 216+432 truncated pentachora
Cells1080+2160 tetrahedra, 1080 truncated tetrahedra
Faces4320 triangles, 720 hexagons
Edges216+2160
Vertices432
Vertex figureRectified-pentachoric pyramid, edge lengths 1 (base), 3 (sides)
Measures (edge length 1)
Circumradius2
Hypervolume
Dipetal anglesTot–tip–tix:
 Hin–pen–tix:
 Hin–hex–tot: 120°
 Tot–tip–tot:
Central density1
Number of external pieces126
Level of complexity18
Related polytopes
ArmyTojak
RegimentTojak
ConjugateNone
Abstract & topological properties
Flag count933120
Euler characteristic0
OrientableYes
Properties
SymmetryE6, order 51840
ConvexYes
NatureTame

The truncated 2 21 polytope or tojak, also called the truncated 221 polytope, is a convex uniform polypeton. It consists of 27 truncated triacontaditera, 27 demipenteracts, and 72 truncated hexatera. 5 truncated triacontaditera, 1 demipenteract, and 5 truncated hexatera join at each vertex. As the name suggests, it is the truncation of the icosiheptaheptacontadipeton.

Gallery[edit | edit source]

Vertex coordinates[edit | edit source]

The vertices of a truncated 2 21 polytope of edge length , centered at the origin, are given by all permutations and even sign changes of the first 5 coordinates of:

  • ,
  • ,
  • ,
  • ,
  • ,
  • .

External links[edit | edit source]