Small cubihexadecadisoctachoron

Small cubihexadecadisoctachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sichado
Coxeter diagram	x3x3o4/3x4*b ()
Elements
Cells	24 cubes, 16 truncated tetrahedra, 8 small cubicuboctahedra, 8 great rhombicuboctahedra
Faces	64 triangles, 48+96 squares, 64 hexagons, 48 octagons
Edges	96+192+192
Vertices	192
Vertex figure	Crossed isosceles trapezoidal pyramid, base edge lengths 1, √2+√2, √2, √2+√2; lateral edge lengths √2, √2, √3, √3
Measures (edge length 1)
Circumradius	${\sqrt {\frac {7+3{\sqrt {2}}}{2}}}\approx 2.37093$
Hypervolume	${\frac {331+188{\sqrt {2}}}{6}}\approx 99.47869$
Dichoral angles	Socco–4–cube: 135°
	Socco–3–tut: 120°
	Socco–8–girco: 90°
	Girco–4–cube: 90°
	Tut–6–girco: 60°
Related polytopes
Army	Prit
Regiment	Prit
Conjugate	Great cubihexadecadisoctachoron
Abstract & topological properties
Flag count	6144
Euler characteristic	–24
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	No
Nature	Tame

The small cubihexadecadisoctachoron, or sichado, is a nonconvex uniform polychoron that consists of 24 cubes, 16 truncated tetrahedra, 8 small cubicuboctahedra, and 8 great rhombicuboctahedra. 1 cube, 1 truncated tetrahedron, 1 small cubicuboctahedron, and 2 great rhombicuboctahedra join at each vertex.

Cross-sections

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the prismatorhombated tesseract.

External links

• Bowers, Jonathan. "Category 10: Prismatorhombates" (#356).

• Klitzing, Richard. "sichado".