The first polyhedron in soccer football

The history of the Soccer World Cups began in 1930 when the first World Cup was carried out in Uruguay, host country and first champion. The rules of this sport were established in England at the end of the XIX century. Since then, the ball was made of leather clusters joined by hand.

The form of the traditional ball changed at the beginning of the 70s when a new geometric model revolutionized the history of this sport.

At the end of this decade, the leather was substituted by the vinyl, a new plastic material. An interesting anecdote is that the old leather balls became heavy when they were wet in the water, can you imagine the knees and feet of the first football players?

The old ball of clusters was joined using curved segments to form a sphere. Diverse models were presented in the following Cups after Uruguay’s but always based on the clusters shape. It was until Mexico 70 when everything changed in the history of the soccer. First of all, the games were first shown in TV and second, a new polyhedral model was introduced for the shape of the ball.

People around the world love soccer but this feeling is not the same for mathematics, isn’t it? However they were intimately bound since 1970.

In the soccer ball presented for Mexico 70, 12 pentagons (almost always in black color) and 20 hexagons (as a rule in white color) could be distinguished for the first time. Each pentagon (regular polygon of 5 sides) is surrounded by 5 hexagons (regular polygon of 6 sides) and the resulting geometric figure is a polyhedron named ‘truncated icosahedron’.

The original icosahedron is a polyhedron formed by 20 equilateral triangle faces and is one of the 5 platonic solids whose faces are always regular polygons. The other 4 platonic solids are: the tetrahedron (4 equilateral triangle faces), the cube (6 squared faces), the octahedron (8 equilateral triangle faces) and the dodecahedron (12 pentagon faces). 

The vertexes of the icosahedron are the points where 3 faces converge at the same time. If they are cut, and we suppose that the icosahedron is solid, the generated figure is the truncated icosahedron, for further visualization: the soccer ball.

The geometric pattern introduced in Mexico 70 by Adidas was named ‘Telstar’ in honor to the satellite rushed at the beginning of the 60s for the intercontinental television transmission (America and Europe).

In 1986, the World Cup was carried out in Mexico again. The promotional poster was a soccer ball in red and white colors, or in other words: a truncated icosahedron in red and white colors!