Applications
The balls used in soccer and team handball are perhaps the best-known example of a spherical polyhedron analog to the truncated icosahedron, found in everyday life. The ball comprises the same pattern of regular pentagons and regular hexagons, but it is more spherical due to the pressure of the air inside and the elasticity of the ball. This ball type was introduced in 1970; starting with the 2006 World Cup, the design has been superseded by newer patterns.
A variation of the icosahedron was used as the basis of the honeycomb wheels (made from a polycast material) used by the Pontiac Motor Division between 1971 to 1976 on its Trans Am and Grand Prix.
This shape was also the configuration of the lenses used for focusing the explosive shock waves of the detonators in both the gadget and Fat Man atomic bombs.
The truncated icosahedron can also be described as a model of the Buckminsterfullerene (fullerene) (C60), or "buckyball," molecule, an allotrope of elemental carbon, discovered in 1985. The diameter of the soccer ball and the fullerene molecule are 22 cm and ca. 1 nm, respectively, hence the size ratio is 220,000,000:1.
The truncated icosahedron is also hypothesized in geology to be the driving force behind many tectonic fabrics on earth. According to the theory, since the shape is a close geometric analog to the shape of the earth, it can explain the trend of many different fracture and associated features in plate tectonic rifting and craton shape.
Read more about this topic: Truncated Icosahedron