Cellirhombidodecateron

Cellirhombidodecateron
(OFF file)
Rank	5
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Card
Coxeter diagram	x3o3x3o3x ()
Elements
Tera	20 triangular duoprisms, 30 cuboctahedral prisms, 12 small rhombated pentachora
Cells	120+120 triangular prisms, 30 octahedra, 90 cubes, 60 cuboctahedra
Faces	120+240 triangles, 180+360 squares
Edges	360+360
Vertices	180
Vertex figure	Antiduowedge, edge lengths 1 (bases of disphenoid cell and top square) and √2 (remaining edges)
Measures (edge length 1)
Circumradius	$\frac{\sqrt{11}}{2} ≈ 1.65831$
Hypervolume	$\frac{161\sqrt{3}}{10} ≈ 27.88602$
Diteral angles	Cope–trip–triddip: 135°
	Srip–co–cope: $\arccos\left(-\frac{\sqrt{10}}{5}\right) ≈ 129.23152°$
	cope–cube–cope: 120°
	Srip–trip–cope: $\arccos\left(-\frac{\sqrt{10}}{10}\right) ≈ 108.43495°$
	Srip–oct–srip: $\arccos\left(-\frac15\right) ≈ 101.53696°$
Central density	1
Number of external pieces	62
Level of complexity	28
Related polytopes
Army	Card
Regiment	Card
Dual	Anticupolanotched hecatonoctacontateron
Conjugate	None
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	A5×2, order 1440
Convex	Yes
Nature	Tame

The cellirhombidodecateron, or card, also called the cellirhombated hexateron or stericantellated 5-simplex, is a convex uniform polyteron. It consists of 20 triangular duoprisms, 30 cuboctahedral prisms, and 12 small rhombated pentachora. 1 triangular duoprism, 2 small rhombated pentachora, and 4 cuboctahedral prisms join at each vertex. As the name suggests, it is the stericantellation of the hexateron.

Vertex coordinates

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

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

Representations

A cellirhombated dodecateron has the following Coxeter diagrams:

• x3o3x3o3x (full symmetry)
• xxxo3xxoo3ooxx3oxxx&#xt (A₄ axial, small rhombated pentachoron-first)
• x(uo)(xd)(uo)x x(xx)(xo)(ou)x3o(xo)(xx)(xo)o3x(ou)(xo)(xx)x&#xt (A₃×A₁ axial, cuboctahedral prism-first)

Gallery

• 

  A₄ orthographic projection

• 

  A₃

• 

  A₂

Related polytopes

The cellirhombidodecateron is the colonel of a regiment of 18 members. Of these, 9 have full symmetry, while the other 9 have single A5 symmetry only.

External links

• Klitzing, Richard. "card".

• Wikipedia Contributors. "Stericantellated 5-simplex".