Celliprismatotruncatododecateron

Celliprismatotruncatododecateron
(OFF file)
Rank	5
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Captid
Coxeter diagram	x3x3o3x3x ()
Elements
Tera	30 truncated tetrahedral prisms, 20 hexagonal duoprisms, 12 prismatorhombated pentachora
Cells	120 triangular prisms, 120+120 hexagonal prisms, 60 truncated tetrahedra, 30 cuboctahedra
Faces	240 triangles, 90+180+360 squares, 240 hexagons
Edges	360+720
Vertices	360
Vertex figure	Rectangular scalene, base edge lengths 1 and √2, remaining edge lengths √2 (5) and √3 (4)
Measures (edge length 1)
Circumradius	$\sqrt5 ≈ 2.23608$
Hypervolume	$\frac{399\sqrt3}{5} ≈ 138.21765$
Diteral angles	Tuttip–hip–hiddip: 135°
	Prip–tut–tuttip: $\arccos\left(-\frac{\sqrt{10}}{5}\right) ≈ 129.23152°$
	Prip–hip–hiddip: $\arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505°$
	Prip–trip–tuttip: $\arccos\left(-\frac{\sqrt{10}}{10}\right) ≈ 108.43495°$
	Prip–co–prip: $\arccos\left(-\frac15\right) ≈ 101.53696°$
Central density	1
Number of external pieces	62
Level of complexity	40
Related polytopes
Army	Captid
Regiment	Captid
Dual	Rhombipyramidal pyramidal triacosihexecontateron
Conjugate	None
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	A5×2, order 1440
Convex	Yes
Nature	Tame

The celliprismatotruncatododecateron, or captid, also called the celliprismatotruncated hexateron or steriruncitruncated 5-simplex, is a convex uniform polyteron. It consists of 30 truncated tetrahedral prisms, 20 hexagonal duoprisms, and 12 prismatorhombated pentachora. 2 prismatorhombated pentachora, 2 truncated tetrahedral prisms, and 2 hexagonal duoprisms join at each vertex. As the name suggests, it is the steriruncitruncation of the hexateron.

Vertex coordinates

The vertices of a celliprismatotruncatododecateron of edge length 1 can be given in 6 dimensions as all permutations of:

• $\left(2\sqrt2,\,\frac{3\sqrt2}{2},\,\sqrt2,\,\sqrt2,\,\frac{\sqrt2}{2},\,0\right).$

Representations

A celliprismatotruncatododecateron has the following Coxeter diagrams:

• x3x3o3x3x (full symmetry)
• xxxux3xxxoo3ooxxx3xuxxx&#xt (A₄ axial, prismatorhombated pentachoron-first)

Gallery

• 

  A₄ orthographic projection

• 

  A₃

• 

  A₂

Related polytopes

The celliprismatotruncatododecateron is the colonel of a three-member regiment that also includes the retrocelliprismatotruncatododecateron and lepidocelliprismatotruncatododecateron.

External links

• Bowers, Jonathan. "Category 13: Prismatorhombates and Kin" (#844).

• Klitzing, Richard. "captid".

• Wikipedia Contributors. "Steriruncitruncated 5-simplex".