Omnitruncated 6-simplex

Omnitruncated 6-simplex
Rank6
TypeUniform
Notation
Bowers style acronymGotaf
Coxeter diagramx3x3x3x3x3x ()
Elements
Peta70 hexagonal-truncated octahedral duoprisms
42 great prismatodecachoric prisms
14 omnitruncated 5-simplices
Tera210+420 square-hexagonal duoprisms
140+280 hexagonal duoprisms
210+210+210 truncated octahedral prisms
42+84 great prismatodecachora
Cells1260+1260 cubes
840+840+840+840+840+840 hexagonal prisms
420+420 truncated octahedra
Faces1260+1260+2520+2520+2520+2520 squares
840+1680+1680 hexagons
Edges5040+5040+5040
Vertices5040
Vertex figureIrregular hexateron
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {14}}\approx 3.74166}$
Hypervolume${\displaystyle {\frac {16807{\sqrt {7}}}{8}}\approx 5558.39279}$
Central density1
Related polytopes
ArmyGotaf
RegimentGotaf
ConjugateNone
Abstract & topological properties
Flag count3628800
Euler characteristic0
OrientableYes
Properties
SymmetryA6×2, order 10080
Flag orbits360
ConvexYes
NatureTame

The omnitruncated 6-simplex, also called the omnitruncated heptapeton or great teritetradecapeton, is a convex uniform 6-polytope. It consists of 14 omnitruncated 5-simplices, 42 great prismatodecachoric prisms, and 70 hexagonal-truncated octahedral duoprisms. 2 omnitruncated 5-simplices, 2 great prismatodecachoric prisms, and 2 hexagonal-truncated octahedral duoprisms join at each vertex. As the name suggests, it is the omnitruncation of the 6-simplex.

It is the 6-dimensional permutohedron.