Disnub icosidodecahedron

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Disnub icosidodecahedron
UC69-2 snub dodecahedra.png
Bowers style acronymDissid
Coxeter diagramCDel node h3.pngCDel 5.pngCDel node h3.pngCDel 3.pngCDel node h3.png
Components2 snub dodecahedra
Faces120 triangles, 40 triangles as 20 hexagrams, 24 pentagons as 12 stellated decagons
Vertex figureFloret pentagon, edge lengths 1, 1, 1, 1, (1+5)/2
Measures (edge length 1)
Circumradius≈ 2.15584
Volume≈ 75.23330
Dihedral angles3–3: ≈ 164.17537°
 5–3: ≈ 152.92992°
Central density2
Number of external pieces392
Level of complexity26
Related polytopes
ArmySemi-uniform Grid
DualCompound of two pentagonal hexecontahedra
ConjugatesGreat disnub icosidodecahedron, great inverted disnub icosidodecahedron, great diretrosnub icosidodecahedron
Convex coreIcosidodecatruncated disdyakis triacontahedron
Abstract & topological properties
Flag count1200
SymmetryH3, order 120

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

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

Measures[edit | edit source]

The circumradius R ≈ 2.15584 of the disnub icosidodecahedron with unit edge length is the largest real root of

Its volume V ≈ 75.23330 is given by the largest real root of

Its dihedral angles may be given as acos(α) for the angle between two triangles, and acos(β) for the angle between a pentagon and a triangle, where α ≈ –0.96210 is the smallest real root of

and β ≈ –0.89045 is the second to smallest root of


External links[edit | edit source]

  1. Wolfram Research, Inc. (2023). "Wolfram|Alpha Knowledgebase". Champaign, IL. "PolyhedronData["SnubDodecahedron", {"Circumradius", "Volume", "DihedralAngles"}]".