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# Small retrosnub icosicosidodecahedron

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 Title: Small retrosnub icosicosidodecahedron Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### 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
(35.5/3)/2
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}.

## Contents

• Convex hull 1
• Cartesian coordinates 2

## 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).