page_title: Truncated icosahedron
section_title: Dimensions
hierarchical_section_title: Truncated icosahedron / Characteristics / Dimensions
context_page_description: 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 has 12 regular pentagonal faces, 20 regular hexagonal faces, 60 vertices and 90 edges.
  It is the Goldberg polyhedron GPV or {5+,3}1,1, containing pentagonal and hexagonal faces.
  This geometry is associated with footballs 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 molecule.
  It is used in the cell-transitive hyperbolic space-filling tessellation, the bitruncated order-5 dodecahedral honeycomb.
context_section_description: If the edge length of a truncated icosahedron is a, the radius of a circumscribed sphere (one that touches the truncated icosahedron at all vertices) is: 
  where φ is the golden ratio.
  This result is easy to get by using one of the three orthogonal golden rectangles drawn into the original icosahedron (before cut off) as the starting point for our considerations. The angle between the segments joining the center and the vertices connected by shared edge (calculated on the basis of this construction) is approximately 23.281446°.
caption: Mutually orthogonal golden rectangles drawn into the original icosahedron (before cut off)