Rank3
TypeUniform
Notation
Bowers style acronymDisdid
Elements
Faces120 triangles, 24 pentagons as 12 stellated decagons, 24 pentagrams 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≈ 36.51284
Dihedral angles5–3: ≈ 157.77792°
3–3: ≈ 151.48799°
5/2–3: ≈ 129.79515°
Central density6
Number of external pieces1092
Level of complexity64
Related polytopes
ArmySemi-uniform Grid
RegimentDisdid
DualCompound of two medial pentagonal hexecontahedra
ConjugateCompound of two inverted snub dodecadodecahedra
Abstract & topological properties
Flag count1200
OrientableYes
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The disnub dodecadodecahedron, disdid, or compound of two 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 snub dodecadodecahedral antiprism, which is four-dimensional.

Measures

The circumradius ${\displaystyle R\approx 1.27444}$ of the disnub dodecadodecahedron with unit edge length is the largest real root of:

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

Its volume ${\displaystyle V\approx 36.51284}$ is given by the largest real root of:

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