Truncated icosahedron

Truncated icosahedron
Type	Archimedean solid Uniform polyhedron Goldberg polyhedron
Faces	32
Edges	90
Vertices	60
Symmetry group	Icosahedral symmetry ${\displaystyle \mathrm {I} _{\mathrm {h} }}$
Dual polyhedron	Pentakis dodecahedron
Vertex figure
Net

In geometry, the truncated icosahedron is an Archimedean solid with 32 faces. It is a polyhedron that may be associated with footballs (soccer balls) typically patterned with white hexagons and black pentagons; the Adidas Telstar was the first soccer ball to use this pattern in the 1970s. 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 an example of a Goldberg polyhedron.

It is used in the cell-transitive hyperbolic space-filling tessellation, the bitruncated order-5 dodecahedral honeycomb.