The Klein Quartic

A Klein quartic made with 24 heptagons (7-sided shapes). In a 4-dimensional space (CP^2), this can be done with regular heptagons, and the shape has 168 symmetries. This is the largest possible for a 3-holed donught! To push the shape down to 3 dimensions destroys most of this symmetry, and distorts the regular heptagons severely. But by doing so we can construct it out of paper!

Instructions and an interactive model in python were made by Tim Hutton. There is now a more symmetric coloring scheme with 8-colors!

8-color base

For much much more, you could start with this article by John Baez. Among other things, he explains where the number 168 comes from, and how it's related to the fact that 1 - 1/2 - 1/3 - 1/7 = 1/42. "So, we see that far from being arbitrary flukes, the numbers 84 and 168 are burnt deep into the fabric of reality."

More papercraft!

[stellated icosahedron] [stellated dodecahedron] [five tetrahedra]

tags: papercraft | mathart

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