Soccer Ball Maths

A Maths teacher recently asked me: “What shapes make up a soccer ball?”.


The traditional design of a soccer ball is based on a solid figure called a truncated icosahedron. From the image above, can you visualise how many black pentagons and white hexagons there is?


A different solid is shown above. It has 20 triangles, 12 pentagons, and 30 squares. What is its correct name? What are the advantages and disadvantages of constructing a soccer ball from this solid shape?

In the 2006 World Cup a new design consisting of 14 curved panels was introduced as shown below. Adidas claims that the new ball is more round, consistent and precise than the old design. Click here to follow the history of WC Soccer balls.


As a young Mathematics teacher in the 1980’s I valued an old copy of:

H.M. Cundy & A.P. Rollett, “Mathematical Models”

mathematical models

If you do not have access to this classic book then try the website: Paper Models of Polyhedra , or the excellent software program small stella.

I would love to hear about your experiences with building polyhedra in the classroom!


About webmaths

I have been teaching Mathematics in Victorian secondary schools for 30 years. I use the www to make my maths lessons better. I hope this blog will give other teachers some ideas to try in their own classes.
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2 Responses to Soccer Ball Maths

  1. dmc says:

    Came across your site trying to solve the following problem. If you’d like to suggest an answer, I’d love to hear it.

    To build a soccer ball from wood, there will be two types of edges, where a pentagon and hexagon meet, and where a hexagon and a hexagon meet. What compound angles would each type require? In other words, since each piece would have a thickness, the interior edges would need to be cut away at what angles to allow the outside edges to meet?

  2. Pingback: Soccer Homework Worksheets | Soccer Training Pro

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