Messi wins the World Cup! It turns out that the 22 players on the field are not playing with the same ball?

Audit expert: Liu Yuhang

PhD, Beijing International Center for Mathematical Research

The 2022 Qatar World Cup, a football event held every four years, ended with Argentina defeating France in a penalty shootout. Messi realized his dream of winning the World Cup, and the final battle went viral on the Internet.

I have to say that football is really attractive. The small ball has become the focus of countless "big ball" fans during this period. Even pseudo fans like me have joined in this football carnival.

However, what we want to talk about today is not the players’ wonderful passes and shots, nor the confusing list of qualifying teams, but the real “protagonist” on this green field - football .

Messi kisses the World Cup Source｜News Photo

Football is not a ball

When talking about the World Cup, most people focus on the confusing list of qualifiers, the exquisite cooperation between teams and every wonderful shot, while football is just a "round ball" on the green field. What many people don't notice is that the ball used in each World Cup is different, and strictly speaking, the appearance of these footballs cannot even be simply summarized as "ball".

Unlike today, when each World Cup has its own exclusive ball , few people cared about the match ball in the early days of this event. The first World Cup in Uruguay didn't even have an official ball. Even the ball for the final was decided by negotiation between the two teams. The Argentine standard ball (Tiento) was used in the first half, and the Uruguayan standard ball (T-Model) was used in the second half. It can be said that it was very "arbitrary".

Tiento (left) and T-Model (right) Source: Wikipedia

After the 1954 World Cup in Switzerland, the World Cup ball gradually came to a unified standard: made of 18 pieces of leather sewn perpendicular to each other. At the same time, the sewing process, materials and production technology were also gradually improved.

The concept of a World Cup "special football" that is now widely accepted by everyone officially entered the public eye after the 1970 World Cup in Mexico. It was also at that World Cup that the well-known black and white block football "Telstar" (Telstar Elast) officially debuted.

Source: Wikipedia

This classic football is made up of 32 faces, including 12 regular pentagons and 20 regular hexagons. This polyhedron is obtained by cutting off all the vertices of a regular icosahedron, so it is called a "truncated icosahedron". While maintaining the rotational symmetry of the regular icosahedron, it adds mirror symmetry. The convexities and seams on the surface just reduce the resistance of the football when it flies in the air.

The official balls for this year's World Cup group stage, " Al Rihla", and the semi-final and final stages, "Al Hilm", have been designed to reduce resistance in the air by improving materials and adding surface depressions. They are claimed to be the fastest, most accurate and stable first-time match balls in World Cup history.

Source | Stadium DB website/Qatar 2022

God likes to play football

The discovery of regular polyhedra has always been regarded as one of the most wonderful and unique discoveries in the history of mathematics. To the surprise of many people, only five regular polyhedra have been discovered so far: tetrahedron (with 4 triangular faces), cube (with 6 square faces), octahedron (with 8 triangular faces), dodecahedron (with 12 pentagonal faces), and icosahedron (with 20 triangular faces).

Plato once linked these five polyhedrons with various elements in the universe, so the ancient Greeks called these five figures "Platonic solids". Euclid proved in his work "Elements of Geometry" that these five regular polyhedrons are the only possible regular polyhedron solid figures.

After studying Platonic solids, Archimedes discovered that by symmetrically cutting off the vertices of a solid, a new type of solid could be obtained, called "Archimedes solids". The planes that make up these solids are still regular polygons, but the number of sides of these polygons is different. The truncated icosahedron, which has been "borrowed" by football in modern times, is one of them.

Source of the truncated icosahedron drawn by Leonardo da Vinci | Illustration of "Divine Proportion"

The truncated icosahedron has 60 vertices, 90 edges, and 32 faces, including 20 regular hexagons and 12 regular pentagons. Every 3 faces intersect at a vertex, that is, every 2 hexagons and 1 pentagon intersect at a vertex. This unique structure has extremely important special significance in many fields such as architecture and chemistry.

Source | Cover of Nature magazine, November 14, 1985

The famous architect Richard Buckminster Fuller used this type of structure extensively in his designs, which not only reduced the use of materials and assembly difficulty, but also increased the stability of the structure. This classic design has attracted the attention of many designers and scientists, the most famous of which is the carbon-60 atom group discovered by Harry Kroto, Richard Smalley and Robert Curl. The structure was confirmed to be a truncated icosahedron. This discovery provided a new way to construct matter at the molecular level, triggering a great revolution in the chemical world. This shape is also called "fullerene" or figuratively called "footballene".

When watching the World Cup, while enjoying the wonderful performances of various stars, you might as well pay some attention to football itself. After all, the unpredictability that the structure of football itself brings to the event also adds unspeakable charm to this sport!