Inverted snub dodecadodecahedron

The inverted snub dodecadodecahedron or isdid, is a uniform polyhedron. It consists of 60 snub triangles, 12 pentagrams, and 12 pentagons. Three triangles, 1 pentagon, and one pentagram meeting at each vertex. It can be constructed by alternation of the quasitruncated dodecadodecahedron and then setting all edge lengths to be equal.

Inverted snub dodecadodecahedron
Inverted snub dodecadodecahedron.png
Bowers style acronymIsdid
Coxeter diagrams5/3s5s (CDel node h.pngCDel 5.pngCDel rat.pngCDel 3x.pngCDel node h.pngCDel 5.pngCDel node h.png)
Faces60 triangles, 12 pentagons, 12 pentagrams
Vertex figureIrregular pentagon, edge lengths 1, 1, (5–1)/2, 1, (1+5)/2
Inverted snub dodecadodecahedron vertfig.png
Measures (edge length 1)
Circumradius≈ 0.85163
Volume≈ 4.61431
Dihedral angles3–3: ≈ 130.49074°
 5–3: ≈ 68.64088°
 5/2–3: ≈ 11.12448°
Central density9
Number of pieces372
Level of complexity39
Related polytopes
ArmyNon-uniform snid
DualMedial inverted pentagonal hexecontahedron
ConjugateSnub dodecadodecahedron
Convex coreDodecahedron
Abstract properties
Euler characteristic-6
Topological properties
SymmetryH3+, order 60


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


Its volume V ≈ 4.61431 is given by the smallest positive real root of:


These same polynomials define the circumradius and volume of the snub dodecadodecahedron.

Related polyhedraEdit

The inverted disnub dodecadodecahedron is a uniform polyhedron compound composed of the 2 opposite chiral forms of the inverted snub dodecadodecahedron.

o5/3o5o truncations
Name OBSA Schläfli symbol CD diagram Picture
Small stellated dodecahedron sissid {5/3,5} x5/3o5o (       )
Quasitruncated small stellated dodecahedron quit sissid t{5/3,5} x5/3x5o (       )
Dodecadodecahedron did r{5,5/3} o5/3x5o (       )
Truncated great dodecahedron tigid t{5,5/3} o5/3x5x (       )
Great dodecahedron gad {5,5/3} o5/3o5x (       )
Complex ditrigonal rhombidodecadodecahedron (degenerate, ditdid+rhom) cadditradid rr{5,5/3} x5/3o5x (       )
Quasitruncated dodecadodecahedron quitdid tr{5,5/3} x5/3x5x (       )
Inverted snub dodecadodecahedron isdid sr{5,5/3} s5/3s5s (       )

External linksEdit