Small snub icosicosidodecahedron

Small snub icosicosidodecahedron
Small snub icosicosidodecahedron.png
Type Uniform star polyhedron
Elements F = 112, E = 180
V = 60 (χ = −8)
Faces by sides (40+60){3}+12{5/2}
Wythoff symbol | 5/2 3 3
Symmetry group Ih, [5,3], *532
Index references U32, C41, W110
Dual polyhedron Small hexagonal hexecontahedron
Vertex figure Small snub icosicosidodecahedron vertfig.png
35.5/2
Bowers acronym Seside

In geometry, the small snub icosicosidodecahedron or snub disicosidodecahedron is a uniform star polyhedron, indexed as U32. It has 112 faces (100 triangles and 12 pentagrams), 180 edges, and 60 vertices. Its stellation core is a truncated pentakis dodecahedron. It also called a holosnub icosahedron, ß{3,5}.

3D model of a small snub icosicosidodecahedron

The 40 non-snub triangular faces form 20 coplanar pairs, forming star hexagons that are not quite regular. Unlike most snub polyhedra, it has reflection symmetries.

Convex hullEdit

Its convex hull is a nonuniform truncated icosahedron.

 
Truncated icosahedron
(regular faces)
 
Convex hull
(isogonal hexagons)
 
Small snub icosicosidodecahedron

Cartesian coordinatesEdit

Cartesian coordinates for the vertices of a small snub 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 alsoEdit

External linksEdit

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