Runcicantitruncated 5-simplex

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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
Hypervolume
Diteral anglesTuttip–trip–thiddip: 135°
 Grip–tut–tuttip:
 Grip–trip–thiddip:
 Gippid–hip–thiddip:
 Gippid–hip–tuttip:
 Gippid–toe–grip:
 Gippid–toe–gippid:
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[edit | edit source]

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

  • .

Gallery[edit | edit source]

External links[edit | edit source]