Truncated icosahedron
In geometry, the truncated icosahedron is an Archimedean solid, one of 13 convex isogonal nonprismatic solids whose 32 faces are two or more types of regular polygons. It is the only one of these shapes that does not contain triangles or squares. In general usage, the degree of truncation is assumed to be uniform unless specified.
| Truncated icosahedron | |
|---|---|
(Click here for rotating model) | |
| Type | Archimedean solid Uniform polyhedron |
| Elements | F = 32, E = 90, V = 60 (χ = 2) |
| Faces by sides | 12{5}+20{6} |
| Conway notation | tI |
| Schläfli symbols | t{3,5} |
| t0,1{3,5} | |
| Wythoff symbol | 2 5 | 3 |
| Coxeter diagram | |
| Symmetry group | Ih, H3, [5,3], (*532), order 120 |
| Rotation group | I, [5,3]+, (532), order 60 |
| Dihedral angle | 6-6: 138.189685° 6-5: 142.62° |
| References | U25, C27, W9 |
| Properties | Semiregular convex |
Colored faces |
5.6.6 (Vertex figure) |
Pentakis dodecahedron (dual polyhedron) |
Net |
It has 12 regular pentagonal faces, 20 regular hexagonal faces, 60 vertices and 90 edges.
It is the Goldberg polyhedron GPV(1,1) or {5+,3}1,1, containing pentagonal and hexagonal faces.
This geometry is associated with footballs (soccer balls) typically patterned with white hexagons and black pentagons. Geodesic domes such as those whose architecture Buckminster Fuller pioneered are often based on this structure. It also corresponds to the geometry of the fullerene C60 ("buckyball") molecule.
It is used in the cell-transitive hyperbolic space-filling tessellation, the bitruncated order-5 dodecahedral honeycomb.