Compound of two small icosicosidodecahedra

Compound of two small icosicosidodecahedra
Rank	3
Type	Compound
Elements
Components	2 small icosicosidodecahedra
Faces	24 triangles, 24 pentagrams, 24 hexagons, 8 golden hexagrams, 8 compound of two hexagons
Edges	72+48+48+48+24
Vertices	24+48+48
Vertex figure	Isosceles trapezoid, edge lengths 1, √3, (√5–1)/2, √3
Measures (edge length 1)
Circumradius	${\sqrt {\frac {17+3{\sqrt {5}}}{8}}}\approx 1.72149$
Volume	$2{\frac {30+29{\sqrt {5}}}{3}}\approx 63.23065$
Dihedral angles	5/2–6: $\arccos \left(-{\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 142.62263^{\circ }$
	3–6: $\arccos \left(-{\frac {\sqrt {5}}{3}}\right)\approx 138.18969^{\circ }$
Central density	4
Related polytopes
Regiment	Compound of two small icosicosidodecahedra
Dual	Compound of two small icosacronic hexecontahedra
Conjugate	Compound of two great icosicosidodecahedra
Convex core	Octatruncated tetrakis hexahedron
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	B3, order 48
Convex	No
Nature	Tame

The compound of two small icosicosidodecahedra is a polyhedron compound. It consists of 40 triangles (16 of which fall into pairs in the same planes, forming 8 golden hexagrams), 24 pentagrams, and 40 hexagons (16 of which form 8 compound of two hexagons). One triangle, two hexagons, and one pentagram (sometimes a hexagram replaces the triangle, or one or more compounds of two hexagons replaces a hexagon) join at each vertex.

Related polytopes

The compound of two small icosicosidodecahedra is one of the facets of some uniform polychora of the sadros daskydox regiment.

Its non-standard hexagram faces are not to be confused with the hexagram faces of the small snub icosicosidodecahedron.