# Stericantitruncated 5-simplex

Stericantitruncated 5-simplex
Rank5
TypeUniform
Notation
Bowers style acronymCograx
Coxeter diagramx3x3x3o3x ()
Elements
Tera20 triangular-hexagonal duoprisms, 15 cuboctahedral prisms, 15 truncated octahedral prisms, 6 great rhombated pentachora, 6 prismatorhombated pentachora
Cells60+60+60 triangular prisms, 90 cubes, 60+60 hexagonal prisms, 30 truncated tetrahedra, 30 cuboctahedra, 30 truncated octahedra
Faces120+120 triangles, 180+180+180+180 squares, 60+120 hexagons
Edges180+180+360+360
Vertices360
Vertex figureSkew rectangular pyramidal pyramid, base edge lengths 1 and 2, remaining edge lengths 2 (6) and 3 (3)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {195}}{6}}\approx 2.32737}$
Hypervolume${\displaystyle {\frac {20297{\sqrt {3}}}{240}}\approx 146.48098}$
Diteral anglesTope–hip–thiddip: 135°
Cope–trip–thiddip: 135°
Prip–co–cope: ${\displaystyle \arccos \left(-{\frac {\sqrt {10}}{5}}\right)\approx 129.23152^{\circ }}$
Grip–toe–tope: ${\displaystyle \arccos \left(-{\frac {\sqrt {10}}{5}}\right)\approx 129.23152^{\circ }}$
Cope–cube–tope: 120°
Prip–trip–thiddip: ${\displaystyle \arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }}$
Grip–trip–cope: ${\displaystyle \arccos \left(-{\frac {\sqrt {10}}{10}}\right)\approx 108.43495^{\circ }}$
Prip–hip–tope: ${\displaystyle \arccos \left(-{\frac {\sqrt {10}}{10}}\right)\approx 108.43495^{\circ }}$
Prip–tut–grip: ${\displaystyle \arccos \left(-{\frac {1}{5}}\right)\approx 101.53696^{\circ }}$
Central density1
Number of external pieces62
Level of complexity80
Related polytopes
ArmyCograx
RegimentCograx
DualDeltopyramidal pyramidal triacosihexecontateron
ConjugateNone
Abstract & topological properties
Flag count57600
Euler characteristic2
OrientableYes
Properties
SymmetryA5, order 720
ConvexYes
NatureTame

The stericantitruncated 5-simplex, also called the celligreatorhombated hexateron or cograx, is a convex uniform 5-polytope. It consists of 20 triangular-hexagonal duoprisms, 15 cuboctahedral prisms, 15 truncated octahedral prisms, 6 great rhombated pentachora, and 6 prismatorhombated pentachora. 1 prismatorhombated pentachoron, 1 cuboctahedral prism, 1 great rhombated pentachoron, 1 triangular-hexagonal duoprism, and 2 truncated octahedral prisms join at each vertex. As the name suggests, it is the stericantitruncation of the 5-simplex.

## Vertex coordinates

The vertices of a stericantitruncated 5-simplex of edge length 1 can be given in 6 dimensions as all permutations of:

• ${\displaystyle \left(2{\sqrt {2}},\,{\frac {3{\sqrt {2}}}{2}},\,{\sqrt {2}},\,{\frac {\sqrt {2}}{2}},\,{\frac {\sqrt {2}}{2}},\,0\right)}$.

## Related polytopes

The stericantitruncated 5-simplex is the colonel of a three-member regiment that also includes the retrocelligreatorhombated hexateron and lepidocelligreatorhombated hexateron.