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Small retrosnub icosicosidodecahedron

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Title: Small retrosnub icosicosidodecahedron  
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Language: English
Subject: Snub polyhedron, Small snub icosicosidodecahedron, Uniform polyhedra, Pentagram, Snub (geometry)
Publisher: World Heritage Encyclopedia

Small retrosnub icosicosidodecahedron

Small retrosnub icosicosidodecahedron
Type Uniform star polyhedron
Elements F = 112, E = 180
V = 60 (χ = −8)
Faces by sides (40+60){3}+12{5/2}
Wythoff symbol |3/2 3/2 5/2
Symmetry group Ih, [5,3], *532
Index references U72, C91, W118
Dual polyhedron Small hexagrammic hexecontahedron
Vertex figure
Bowers acronym Sirsid

In geometry, the small retrosnub icosicosidodecahedron or small inverted retrosnub icosicosidodecahedron is a nonconvex uniform polyhedron, indexed as U72. It is also called a retroholosnub icosahedron, ß{3/2,5}.


  • Convex hull 1
  • Cartesian coordinates 2
  • See also 3
  • External links 4

Convex hull

Its convex hull is a nonuniform truncated dodecahedron.

truncated dodecahedron

Convex hull

Small retrosnub icosicosidodecahedron

Cartesian coordinates

Cartesian coordinates for the vertices of a small retrosnub icosicosidodecahedron are all the even permutations of

(±(1-ϕ−α), 0, ±(3−ϕα))
(±(ϕ-1−α), ±2, ±(2ϕ-1−ϕα))
(±(ϕ+1−α), ±2(ϕ-1), ±(1−ϕα))

where ϕ = (1+√5)/2 is the golden ratio and α = √(3ϕ−2).

See also

External links

  • Weisstein, Eric W., "Small retrosnub icosicosidodecahedron", MathWorld.
  • Richard Klitzing, 3D star, small retrosnub icosicosidodecahedron

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