# Runcicantitruncated 5-simplex

(Redirected from Great prismated hexateron)
Runcicantitruncated 5-simplex
Rank5
TypeUniform
Notation
Bowers style acronymGippix
Coxeter diagramx3x3x3x3o ()
Elements
Tera20 triangular-hexagonal duoprisms, 15 truncated tetrahedral prisms, 6 great rhombated pentachora, 6 great prismatodecachora
Cells60+60 triangular prisms, 60+60 hexagonal prisms, 30 truncated tetrahedra, 15+30 truncated octahedra
Faces120 triangles, 90+180+180 squares, 60+60+120 hexagons
Edges180+180+180+360
Vertices360
Vertex figureSphenoidal pyramid, edge lengths 1 (1), 2(5), and 3 (4)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {2{\sqrt {15}}}{3}}\approx 2.58199}$
Hypervolume${\displaystyle {\frac {24997{\sqrt {3}}}{240}}\approx 180.40031}$
Diteral anglesTuttip–trip–thiddip: 135°
Grip–tut–tuttip: ${\displaystyle \arccos \left(-{\frac {\sqrt {10}}{5}}\right)\approx 129.23152^{\circ }}$
Grip–trip–thiddip: ${\displaystyle \arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }}$
Gippid–hip–thiddip: ${\displaystyle \arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }}$
Gippid–hip–tuttip: ${\displaystyle \arccos \left(-{\frac {\sqrt {10}}{10}}\right)\approx 108.43495^{\circ }}$
Gippid–toe–grip: ${\displaystyle \arccos \left(-{\frac {1}{5}}\right)\approx 101.53696^{\circ }}$
Gippid–toe–gippid: ${\displaystyle \arccos \left({\frac {1}{5}}\right)\approx 78.46304^{\circ }}$
Central density1
Number of external pieces47
Level of complexity60
Related polytopes
ArmyGippix
RegimentGippix
DualSphenoidal-pyramidal triacosihexecontateron
ConjugateNone
Abstract & topological properties
Flag count43200
Euler characteristic2
OrientableYes
Properties
SymmetryA5, order 720
ConvexYes
NatureTame

The runcicantitruncated 5-simplex, also called the great prismated hexateron or gippix, is a convex uniform 5-polytope. It consists of 20 triangular-hexagonal duoprisms, 15 truncated tetrahedral prisms, 6 great rhombated pentachora, and 6 great prismatodecachora. 2 great prismatodecachora, 1 great rhombated pentachoron, 1 truncated tetrahedral prism, and 1 triangular-hexagonal duoprism join at each vertex. As the name suggests, it is the runcicantitruncation of the 5-simplex.

## Vertex coordinates

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

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