Cube atop small rhombicuboctahedron

Cube atop small rhombicuboctahedron
(OFF file)
Rank	4
Type	Segmentotope
Notation
Bowers style acronym	Cubasirco
Coxeter diagram	xx4oo3ox&#x
Elements
Cells	8 tetrahedra, 12 triangular prisms, 1+6 cubes, 1 small rhombicuboctahedron
Faces	8+24 triangles, 6+6+12+24 squares
Edges	12+24+24+24
Vertices	8+24
Vertex figures	8 triangular antipodiums, edge lengths 1 (base 1) and √2 (base 2 and sides)
	24 isosceles trapezoidal pyramids, base edge lengths 1, √2, √2, √2, side edge lengths 1, 1, √2. √2
Measures (edge length 1)
Circumradius	${\sqrt {\frac {3+{\sqrt {2}}}{2}}}\approx 1.48563$
Hypervolume	${\frac {19+12{\sqrt {2}}}{12}}\approx 2.99755$
Dichoral angles	Tet–3–trip: 150°
	Cube–4–trip: $\arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }$
	Cube–4–cube: 135°
	Sirco–3–tet: 60°
	Sirco–4–trip: $\arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }$
	Sirco–4–cube: 45°
Height	${\frac {\sqrt {2}}{2}}\approx 0.70711$
Central density	1
Related polytopes
Army	Cubasirco
Regiment	Cubasirco
Dual	Octahedral-deltoidal icositetrahedral tegmoid
Conjugate	Cube atop quasirhombicuboctahedron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B3×I, order 48
Convex	Yes
Nature	Tame

The cube atop small rhombicuboctahedron, or cubasirco, is a CRF segmentochoron (designated K-4.71 on Richard Klitzing's list). As the name suggests, it consists of a cube and a small rhombicuboctahedron as bases, connected by 8 tetrahedra, 12 triangular prisms, and 6 further cubes.

It is also sometimes referred to as a cubic cupola, as one generalization of the definition of a cupola is to have a polytope atop an expanded version.

A small disprismatotesseractihexadecachoron can be formed by attaching cube atop small rhombicuboctahedron segmentochora to the bases of the small rhombicuboctahedral prism.

Segmentochoron display

• 

  Cube atop small rhombicuboctahedron

Vertex coordinates

Coordinates for the vertices of a cube atop small rhombicuboctahedron of edge length 1 are given by:

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

along with all permutations of the first three coordinates of:

• $\left(\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0\right).$

External links

• Klitzing, Richard. "cubasirco".
• Wikipedia contributors. "Cubic cupola".