Cuboctahedron atop small rhombicuboctahedron

Cuboctahedron atop small rhombicuboctahedron
(OFF file)
Rank	4
Type	Segmentotope
Notation
Bowers style acronym	Coasirco
Coxeter diagram	ox4xo3ox&#x
Elements
Cells	12 square pyramids, 8 octahedra, 6 square antiprisms, 1 cuboctahedron, 1 small rhombicuboctahedron
Faces	8+8+24+24+24 triangles, 6+6+12 squares
Edges	24+24+24+48
Vertices	12+24
Vertex figures	12 rectangular-square trapezoprisms, one base a rectangle of edge lengths 1 and √2, other base a square of edge length 1, side lengths 1
	24 skewed wedges, edge lengths 1 (6) and √2 (3)
Measures (edge length 1)
Circumradius	${\frac {{\sqrt {7}}+2{\sqrt {14}}}{7}}\approx 1.44701$
Hypervolume	${\frac {\sqrt {103+74{\sqrt {2}}}}{4}}\approx 3.60253$
Dichoral angles	Oct–3–squippy: $\arccos \left({\frac {1-3{\sqrt {2}}}{4}}\right)\approx 144.16048^{\circ }$
	Oct–3–squap: $\arccos \left(-{\frac {\sqrt {4+3{\sqrt {2}}}}{4}}\right)\approx 135.86903^{\circ }$
	Squippy–3–squap: $\arccos \left(-{\frac {\sqrt {4+3{\sqrt {2}}}}{4}}\right)\approx 135.86903^{\circ }$
	Co-4-squap: $\arccos \left(-{\frac {\sqrt[{4}]{2}}{2}}\right)\approx 126.48438^{\circ }$
	Co–3–oct: $\arccos \left({\frac {2-3{\sqrt {2}}}{4}}\right)\approx 124.10147^{\circ }$
	Sirco–4–squippy: $\arccos \left({\frac {2-{\sqrt {2}}}{2}}\right)\approx 72.96875^{\circ }$
	Sirco–3–oct: $\arccos \left({\frac {3{\sqrt {2}}-2}{4}}\right)\approx 55.89854^{\circ }$
	Sirco-4-squap: $\arccos \left({\frac {\sqrt[{4}]{2}}{2}}\right)\approx 53.51562^{\circ }$
Height	${\frac {\sqrt {2{\sqrt {2}}-1}}{2}}\approx 0.67610$
Central density	1
Related polytopes
Army	Coasirco
Regiment	Coasirco
Dual	Rhombic dodecahedral-deltoidal icositetrahedral tegmoid
Conjugate	Cuboctahedron atop small rhombicuboctahedron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B3×I, order 48
Convex	Yes
Nature	Tame

The cuboctahedron atop small rhombicuboctahedron, or coasirco, is a CRF segmentochoron (designated K-4.61 on Richard Klitzing's list). As the name suggests, it consists of a cuboctahedron and a small rhombicuboctahedron as bases, connected by 8 octahedra, 12 square pyramids, and 6 square antiprisms.

Vertex coordinates

The vertices of a cuboctahedron atop small rhombicuboctahedron segmentochoron of edge length 1 are given by:

• $\left(\pm {\frac {\sqrt {2}}{2}},\,\pm {\frac {\sqrt {2}}{2}},\,0,\,{\frac {\sqrt {2{\sqrt {2}}-1}}{2}}\right)$ and all permutations of first three coordinates
• $\left(\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0\right)$ and all permutations of first three coordinates

External links

• Klitzing, Richard. "coasirco".