Soccer Ball Symmetry

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David Swart: Soccer Ball Symmetry. In: Bridges 2015. Pages 151–158



Among the most recognizable sport ball designs are soccer balls with twelve black pentagons and twenty white hexagons. However, soccer ball manufacturers are now exploring a wide variety of new patterns for both their panel designs and graphics. This paper surveys many existing soccer ball designs; it hopes to show how varied they have become and suggests that these designs may serve as an inspiration for other spherical art. Also, this paper promotes modern soccer balls as ideal toy examples to learn and teach various branches of spherical mathematics such as spherical symmetry, group theory, and tessellations.

Extended Abstract


 author      = {David Swart},
 title       = {Soccer Ball Symmetry},
 pages       = {151--158},
 booktitle   = {Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture},
 year        = {2015},
 editor      = {Kelly Delp, Craig S. Kaplan, Douglas McKenna and Reza Sarhangi},
 isbn        = {978-1-938664-15-1},
 issn        = {1099-6702},
 publisher   = {Tessellations Publishing},
 address     = {Phoenix, Arizona},
 note        = {Available online at \url{ }},
 url         = { },

Used References

[1] J. H. Conway, H. Burgiel, C. Goodman-Strauss. The Symmetries of Things. A.K. Peters. 2008.

[2] K. Delp, W. Thurston. Playing with Surfaces: Spheres, Monkey Pants, and Zippergons. In Bridges 2011: Mathematics, Music, Art, Architecture, Culture: 1-8. 2011.

[3] Y.-J. Fan, B.-Y. Jin. From the "Brazuca" ball to Octahedral Fullerenes: Their Construction and Classification. arXiv:1406.7058v1. 2014.

[4] G. Hart. Goldberg Polyhedra. In Shaping Space, 2nd ed. 125-138. Springer. 2012.

[5] V. Hart. Orbifold and Cut. In Bridges 2013: Mathematics, Music, Art, Architecture, Culture: 635-638. 2013

[6] C. Kaplan, B. Bosch. TSP Art. In Bridges 2005: Mathematics, Music, Art, Culture: 301-308. 2005.

[7] P. Pesti. (as of March 29, 2015)

[8] C. Yackel. Teaching Temari: Geometrically Embroidered Spheres in the Classroom. In Bridges 2012: Mathematics, Music, Art, Architecture, Culture: 563-566. 2012.


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