Small snub icosicosidodecahedron

Small snub icosicosidodecahedron
TypeUniform star polyhedron
ElementsF = 112, E = 180
V = 60 (χ = 8)
Faces by sides(40+60){3}+12{5/2}
Wythoff symbol|5/2 3 3
Symmetry groupIh, [5,3], *532
Index referencesU32, C41, W110
Dual polyhedronSmall hexagonal hexecontahedron
Vertex figure
35.5/2
Bowers acronymSeside

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}.

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

Convex hull

Its convex hull is a nonuniform truncated icosahedron.


Truncated icosahedron
(regular faces)

Convex hull
(isogonal hexagons)

Small snub icosicosidodecahedron

Cartesian coordinates

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 also

External links


This article is issued from Wikipedia - version of the 6/8/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.