# soccer balls, pentagons, hexagons

**URL:** <https://boards.straightdope.com/t/soccer-balls-pentagons-hexagons/138496>\
**Category:** Factual Questions\
**Created:** [November 24, 2002, 4:40pm UTC](https://boards.straightdope.com/t/soccer-balls-pentagons-hexagons/138496 "2002-11-24T16:40:24Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![The\_Flying\_Dutchman](https://avatars.discourse-cdn.com/v4/letter/t/9fc348/32.png) [@The\_Flying\_Dutchman](https://boards.straightdope.com/u/The_Flying_Dutchman)\
**Post date:** [November 24, 2002, 4:40pm UTC](https://boards.straightdope.com/t/soccer-balls-pentagons-hexagons/138496/1 "2002-11-24T16:40:24Z")

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My daughter left her soccer ball on the floor of the bathroom last night, and as a result I was able to study the stitch pattern as I performed the morning ritual on the throne.

I noticed a pattern around each hexagonal patch of alternating equivalent hexagons and equilateral pentagons.

Is it mathematically assured that if I perfectly draw hexagons and pentagons on a sphere in the above pattern with equilateral sides, that I will “close” perfectly? Or is some fudging required to make a soccer ball?

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**Author:** ![Tuco](https://avatars.discourse-cdn.com/v4/letter/t/46a35a/32.png) [@Tuco](https://boards.straightdope.com/u/Tuco)\
**Post date:** [November 24, 2002, 4:52pm UTC](https://boards.straightdope.com/t/soccer-balls-pentagons-hexagons/138496/2 "2002-11-24T16:52:08Z")

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No fudging required - this pattern also exists in nature in the form of Carbon-60: the [buckminsterfullerene](http://dheera.net/physics/buckyballs.shtml).

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**Author:** ![andy\_fl](https://avatars.discourse-cdn.com/v4/letter/a/49beb7/32.png) [@andy\_fl](https://boards.straightdope.com/u/andy_fl)\
**Post date:** [November 24, 2002, 5:11pm UTC](https://boards.straightdope.com/t/soccer-balls-pentagons-hexagons/138496/3 "2002-11-24T17:11:16Z")

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The mathematical solution is twelve pentagons and twenty hexagons. The proof is given here - [Solution to the polyhedron football problem in issue 4.2](http://uzweb.uz.ac.zw/science/maths/zimaths/43/zim42sol.htm).

I’ve heard that bees use the same kindof pattern for their hives.

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**Author:** ![23skidoo](https://avatars.discourse-cdn.com/v4/letter/2/f04885/32.png) [@23skidoo](https://boards.straightdope.com/u/23skidoo)\
**Post date:** [November 24, 2002, 7:03pm UTC](https://boards.straightdope.com/t/soccer-balls-pentagons-hexagons/138496/4 "2002-11-24T19:03:54Z")

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It’s called a truncated icosahedron by some, and you can see how closely it resembles a soccerball [here](http://mathworld.wolfram.com/TruncatedIcosahedron.html).