Editing Truncated icosahedron (section)

== Construction ==
The truncated icosahedron can be constructed from a [[regular icosahedron]] by cutting off all of its vertices, known as [[Truncation (geometry)|truncation]]. Each of the 12 vertices at the one-third mark of each edge creates 12 pentagonal faces and transforms the original 20 triangle faces into regular hexagons.{{r|co}} Therefore, the resulting polyhedron has 32 faces, 90 edges, and 60 vertices.{{r|berman}} A [[Goldberg polyhedron]] is one whose faces are 12 pentagons and some multiple of 10 hexagons.  There are three classes of Goldberg polyhedron, one of them is constructed by truncating all vertices repeatedly, and the truncated icosahedron is one of them, denoted as <math> \operatorname{GP}(1,1) </math>.{{r|hart}}