Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymIdisdid
Elements
Faces120 triangles, 24 pentagons as 12 stellated decagons, 24 pentagarms as 12 stellated decagrams
Edges60+120+120
Vertices120
Vertex figureIrregular pentagon, edge lengths 1, 1, (5–1)/2, 1, (1+5)/2
Measures (edge length 1)
Volume≈ 9.22862
Dihedral angles3–3: ≈ 130.49074°
5–3: ≈ 68.64088
5/2–3: ≈ 11.12448°
Central density18
Related polytopes
ArmySemi-uniform Grid
RegimentIdisdid
DualCompound of two medial inverted pentagonal hexecontahedra
Convex coreDodecahedron
Abstract & topological properties
OrientableYes
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The inverted disnub dodecadodecahedron, idisdid, or compound of two inverted snub dodecadodecahedra is a uniform polyhedron compound. It consists of 120 snub triangles, 24 pentagons, and 24 pentagrams (the latter two can combine in pairs due to faces in the same plane). Three triangles, one pentagon, and one pentagram join at each vertex.

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

## Measures

The circumradius R ≈ 0.85163 of the inverted disnub dodecadodecahedron with unit edge length is the smallest positive real root of:

${\displaystyle 64x^8-192x^6+180x^4-65x^2+8.}$

Its volume V ≈ 9.22862 is given by the smallest positive real root of:

${\displaystyle x^8-1340x^6+4525x^4+5895625x^2+240250000.}$