Steritruncated 5-simplex

Steritruncated 5-simplex
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Cappix
Coxeter diagram	x3x3o3o3x ()
Elements
Tera	15 tetrahedral prisms, 20 triangular-hexagonal duoprisms, 6 truncated pentachora, 15 truncated tetrahedral prisms, 6 small prismatodecachora
Cells	30+30 tetrahedra, 60+60+60 triangular prisms, 60 hexagonal prisms, 30 truncated tetrahedra
Faces	120+120 triangles, 90+180 squares, 60 hexagons
Edges	60+180+180
Vertices	120
Vertex figure	Skew triangular antiprismatic pyramid, edge lengths 1 (base triangles), √2 (sides of antiprism and lacings to one base), and √3 (lacings to other base)
Measures (edge length 1)
Circumradius	${\frac {2{\sqrt {6}}}{3}}\approx 1.63299$
Hypervolume	${\frac {1297{\sqrt {3}}}{120}}\approx 18.72058$
Diteral angles	Tuttip–hip–thiddip: 135°
	Tepe–trip–thiddip: 135°
	Tip–tut–tuttip: $\arccos \left(-{\frac {\sqrt {10}}{5}}\right)\approx 129.23152^{\circ }$
	Spid–tet–tepe: $\arccos \left(-{\frac {\sqrt {10}}{5}}\right)\approx 129.23152^{\circ }$
	Spid–trip–thiddip: $\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
	Spid–trip–tuttip: $\arccos \left(-{\frac {\sqrt {10}}{10}}\right)\approx 108.43495^{\circ }$
	Spid–tet–tip: $\arccos \left(-{\frac {1}{5}}\right)\approx 101.53696^{\circ }$
Central density	1
Number of external pieces	62
Level of complexity	40
Related polytopes
Army	Cappix
Regiment	Cappix
Dual	Triangular-antitegmatic pyramidal hecatonicosateron
Conjugate	None
Abstract & topological properties
Flag count	28800
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	A5, order 720
Convex	Yes
Nature	Tame

The steritruncated 5-simplex, also called the celliprismated hexateron or cappix, is a convex uniform 5-polytope. It consists of 15 tetrahedral prisms, 20 triangular-hexagonal duoprisms, 15 truncated tetrahedral prisms, 6 truncated pentachora, and 6 small prismatodecachora. One small prismatodecachoron, 1 tetrahedral prism, 1 truncated pentachoron, 3 truncated tetrahedral prisms, and 3 triangular-hexagonal duoprisms join at each vertex. As the name suggests, it is the steritruncation of the 5-simplex.

Vertex coordinates

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

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

Representations

A steritruncated 5-simplex has the following Coxeter diagrams:

• x3x3o3o3x () (full symmetry)
• xuxx3ooxx3oooo3xxxo&#xt (A₄ axial, small prismatodecachoron-first)

Gallery

• 

  A₄ orthographic projection

• 

  A₃

• 

  A₂

Related polytopes

The steritruncated 5-simplex is the colonel of a regiment of 7 members.

External links

• Klitzing, Richard. "cappix".
• Wikipedia contributors. "Steritruncated 5-simplex".