Steritruncated 5-cube

Steritruncated 5-cube
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Capt
Coxeter diagram	x4x3o3o3x ()
Elements
Tera	80 tetrahedral prisms, 80 triangular-octagonal duoprisms, 32 small prismatodecachora, 40 truncated cubic prisms, 10 truncated tesseracts
Cells	160+160 tetrahedra, 320+320+320 triangular prisms, 240 octagonal prisms, 80 truncated cubes
Faces	640+640 triangles, 480+960 squares, 240 octagons
Edges	320+960+960
Vertices	640
Vertex figure	Skew triangular antiprismatic pyramid, edge lengths 1 (base triangles), √2 (sides of antiprism and lacings to one base), and √2+√2 (lacings to other base)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {19+10{\sqrt {2}}}}{2}}\approx 2.87846$
Hypervolume	${\frac {1471+1024{\sqrt {2}}}{6}}\approx 486.52578$
Diteral angles	Spid–tet–tepe: $\arccos \left(-{\frac {2{\sqrt {5}}}{5}}\right)\approx 153.43495^{\circ }$
	Tepe–trip–todip: 150°
	Ticcup–op–todip: $\arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }$
	Spid–trip–todip: $\arccos \left(-{\frac {\sqrt {15}}{5}}\right)\approx 140.76848^{\circ }$
	Tat–tic–ticcup: 135°
	Spid–trip–ticcup: $\arccos \left(-{\frac {\sqrt {10}}{5}}\right)\approx 129.23152^{\circ }$
	Tat–tet–spid: $\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
Central density	1
Number of external pieces	242
Level of complexity	40
Related polytopes
Army	Capt
Regiment	Capt
Dual	Great triangular-antitegmatic pyramidal hexacositetracontateron
Conjugate	Quasicelliprismated triacontaditeron
Abstract & topological properties
Flag count	153600
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B5, order 3840
Convex	Yes
Nature	Tame

The steritruncated 5-cube, also called the celliprismated triacontaditeron or capt, is a convex uniform 5-polytope. It consists of 80 tetrahedral prisms, 80 triangular-octagonal duoprisms, 40 truncated cubic prisms, 10 truncated tesseracts, and 32 small prismatodecachora. One small prismatodecachoron, 1 truncated tesseract, 1 tetrahedral prism, 3 truncated cubic prisms, and 3 triangular-octagonal duoprisms join at each vertex. As the name suggests, it is the steritruncation of the 5-cube.

Vertex coordinates

The vertices of a steritruncated 5-cube of edge length 1 are given by all permutations of:

• $\left(\pm {\frac {1+2{\sqrt {2}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}}\right)$.

Gallery

• 

  B₄ or D₅ orthographic projection

• 

  B₃, D₄, or A₂

• 

  B₂

• 

  A₃

Related polytopes

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

External links

• Klitzing, Richard. "capt".
• Wikipedia contributors. "Steritruncated 5-cube".