# Steriruncicantic 5-cube

(Redirected from Great prismatodemipenteract)
Steriruncicantic 5-cube
Rank5
TypeUniform
Notation
Bowers style acronymGiphin
Coxeter diagramx3x3x3x *b3o ()
Elements
Tera40 truncated tetrahedral prisms, 16 great rhombated pentachora, 10 tesseractihexadecachora, 16 great prismatodecachora
Cells160 triangular prisms, 80+160 hexagonal prisms, 80+80 truncated tetrahedra, 80+80 truncated octahedra
Faces320 triangles, 240+240+480 squares, 160+320+320 hexagons
Edges480+480+480+960
Vertices960
Vertex figureSphenoidal pyramid, edge lengths 1 (1), 2(4), and 3 (5)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {170}}{4}}\approx 3.25960}$
Hypervolume${\displaystyle {\frac {86647{\sqrt {2}}}{120}}\approx 1021.14469}$
Diteral anglesGrip–trip–tuttip: ${\displaystyle \arccos \left(-{\frac {\sqrt {15}}{5}}\right)\approx 140.76848^{\circ }}$
Tah–tut–tuttip: 135°
Gippid–hip–tuttip: ${\displaystyle \arccos \left(-{\frac {\sqrt {10}}{5}}\right)\approx 129.23152^{\circ }}$
Grip–toe–gippid: ${\displaystyle \arccos \left(-{\frac {3}{5}}\right)\approx 126.86990^{\circ }}$
Tah–toe–grip: ${\displaystyle \arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }}$
Tah–tut–grip: ${\displaystyle \arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }}$
Gippid–hip–gippid: ${\displaystyle \arccos \left(-{\frac {1}{5}}\right)\approx 101.53696^{\circ }}$
Central density1
Number of external pieces82
Level of complexity60
Related polytopes
ArmyGiphin
RegimentGiphin
DualSphenoidal-pyramidal enneacosihexecontateron
ConjugateNone
Abstract & topological properties
Flag count115200
Euler characteristic2
OrientableYes
Properties
SymmetryD5, order 1920
ConvexYes
NatureTame

The steriruncicantic 5-cube, also called the great prismatodemipenteract or giphin, is a convex uniform 5-polytope. It consists of 40 truncated tetrahedral prisms, 16 great rhombated pentachora, 10 tesseractihexadecachora, and 16 great prismatodecachora. 2 great prismatodecachora, 1 great rhombated pentachoron, 1 tesseractihexadecachoron, and 1 trunctaed tetrahedral prism join at each vertex. It can be formed from an alternated faceting of the stericantitruncated 5-orthoplex.

## Vertex coordinates

The vertices of a steriruncicantic 5-cube of edge length 1 are given by all permutations and even sign changes of:

• ${\displaystyle \left({\frac {7{\sqrt {2}}}{4}},\,{\frac {5{\sqrt {2}}}{4}},\,{\frac {3{\sqrt {2}}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}}\right)}$.

## Representations

A steriruncicantic 5-cube has the following Coxeter diagrams:

• x3x3x3x *b3o () (full symmetry)
• s4o3x3x3x () (as alternated faceting)