Compound of two cuboctahedra

Compound of two cuboctahedra
Rank	3
Type	Orbiform
Elements
Components	2 cuboctahedra
Faces	4 triangles (as 2 golden hexagrams), 12 triangles, 12 squares
Edges	12+12+24
Vertices	12+12
Vertex figure	Rectangle, edge lengths 1 and √2
Measures (edge length 1)
Circumradius	$1$
Volume	${\frac {10{\sqrt {2}}}{3}}\approx 4.71405$
Dihedral angle	$\arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }$
Central density	2
Related polytopes
Dual	Compound of two rhombic dodecahedra
Conjugate	None
Convex hull	Hexagonal orthobicupola
Convex core	Variant of orchid 13
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	(G2×A1)/2, order 12
Convex	No
Nature	Tame

The compound of two cuboctahedra is a polyhedron compound. It consists of 16 triangles (4 of which lie in the same two planes at the top and bottom of the shape, forming 2 golden hexagrams) and 12 squares. Two triangles (sometimes one triangle and one hexagram) and two squares join at each vertex.

Related polytopes

The compound of two cuboctahedra is one of the facets of some uniform polychora of the sadros daskydox and gadros daskydox regiments.

It also has the same non-standard hexagram faces as the compound of two icosahedra and its conjugate, the compound of two great icosahedra. These are not to be mistaken for the hexagram faces of the small snub icosicosidodecahedron, though.