# Compound of two snub icosidodecadodecahedra

Rank3
TypeUniform
Notation
Bowers style acronymDesided
Elements
Faces120 triangles, 40 triangles as 20 hexagrams, 24 pentagons as 12 stellated decagons, 24 pentagrams as 12 stellated decagrams
Edges120+120+120
Vertices120
Vertex figureIrregular hexagon, edge lengths 1, 1, 1, (5–1)/2, 1, (1+5)/2
Measures (edge length 1)
Volume≈ 29.28396
Dihedral angles3–3: ≈ 146.78125°
5–3: ≈ 120.43401°
5/2–3: ≈ 7.35214°
Central density8
Number of external pieces752
Level of complexity47
Related polytopes
ArmySemi-uniform Grid
RegimentDesided
DualCompound of two medial hexagonal hexecontahedra
Convex coreDodecahedron
Abstract & topological properties
Flag count1440
OrientableYes
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The disnub icosidodecadodecahedron, desided, or compound of two snub icosidodecadodecahedra is a uniform polyhedron compound. It consists of 120 snub triangles, 40 further triangles, 24 pentagons, and 24 pentagrams (the latter three can combine in pairs due to faces in the same plane). Four triangles, one pentagon, and one pentagram join at each vertex.

Its quotient prismatic equivalent is the snub icosidodecadodecahedral antiprism, which is four-dimensional.

## Measures

The circumradius ${\displaystyle R\approx 1.12690}$ of the disnub icosidodecadodecahedron with unit edge length is the greatest real root of

${\displaystyle 64x^{6}-128x^{4}+68x^{2}-11.}$

Its volume ${\displaystyle V\approx 29.28396}$ is given by the positive real root of

${\displaystyle 729x^{6}-622080x^{4}-162000x^{2}-2121800000.}$