Compound of two great ditrigonal dodecicosidodecahedra

Compound of two great ditrigonal dodecicosidodecahedra
Rank	3
Type	Compound
Elements
Components	2 great ditrigonal dodecicosidodecahedra
Faces	24 triangles, 24 pentagrams, 24 decagrams, 8 golden hexagrams
Edges	120+72+48
Vertices	72+48
Vertex figure	Isosceles trapezoid, edge lengths 1, √(5–√5)/2, (1+√5)/2, √(5–√5)/2
Measures (edge length 1)
Circumradius	${\sqrt {\frac {17-3{\sqrt {5}}}{8}}}\approx 1.13423$
Volume	$7{\frac {15-{\sqrt {5}}}{3}}\approx 29.78251$
Dihedral angles	3–10/3: $\arccos \left(-{\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 142.62263^{\circ }$
	5–10/3: $\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
Central density	8
Related polytopes
Regiment	Compound of two great ditrigonal dodecicosidodecahedra
Dual	Compound of two great ditrigonal dodecacronic hexecontahedra
Conjugate	Compound of two small ditrigonal dodecicosidodecahedra
Convex hull	Semi-uniform great rhombicuboctahedron augmented with square cupolas and ditrigonal frustums
Convex core	Tetrakis hexahedron
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	B3, order 48
Convex	No
Nature	Tame

The compound of two great ditrigonal dodecicosidodecahedra 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 24 decagrams. One triangle, one pentagram, and two decagrams (sometimes a hexagram replaces the triangle) join at each vertex.

Related polytopes

The compound of two great ditrigonal dodecicosidodecahedra is one of the facets of some uniform polychora of the gadros daskydox regiment.

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