Compound of two inverted snub dodecadodecahedra

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Compound of two inverted snub dodecadodecahedra
Rank3
TypeUniform
Notation
Bowers style acronymIdisdid
Elements
Components2 inverted snub dodecadodecahedra
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)
Circumradius≈ 0.85163
Volume≈ 9.22862
Dihedral angles3–3: ≈ 130.49074°
 5–3: ≈ 68.64088
 5/2–3: ≈ 11.12448°
Central density18
Number of external pieces1752
Level of complexity112
Related polytopes
ArmySemi-uniform Grid
RegimentIdisdid
DualCompound of two medial inverted pentagonal hexecontahedra
ConjugateCompound of two snub dodecadodecahedra
Convex coreDodecahedron
Abstract & topological properties
Flag count1200
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[edit | edit source]

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

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

External links[edit | edit source]