Recognised as Polyhedron
Truncated icosahedron
- Archimedean
- 32 faces
- Dual: pentakis dodecahedron
The truncated icosahedron is a Archimedean solid with 32 faces, 90 edges and 60 vertices: 12 pentagons and 20 hexagons. Its dual is the pentakis dodecahedron, and its dihedral angle is 142.623°. It is the shape of a traditional football, and of buckminsterfullerene.
Faces, edges and vertices
Faces3212 pentagons and 20 hexagons
Edges90
Vertices60
Euler characteristicV − E + F = 60 − 90 + 32 = 2every convex polyhedron gives 2
FamilyArchimedeansemi-regular: regular faces of more than one kind, identical vertices
Dual polyhedronpentakis dodecahedron
Measurements at edge length 1
Volume55.287731cubic units for a unit edge
Surface area72.607253square units for a unit edge
Dihedral angle142.623°the angle between two adjacent faces
Volume at edge 1055,287.7308
Surface area at edge 107,260.7253
Isoperimetric ratio0.903171 for a sphere; higher means more efficiently packed
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