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It's actually a Riemann surface, the most symmetrical Riemann surface with 4 holes! We're seeing it as a branched cover of the sphere. But you can also build it by taking a tiling of the hyperbolic plane by pentagons, and modding out by a certain group action. (6/n)pic.twitter.com/4sZVtzP56s
Most of this stuff - and more - was discovered by Felix Klein in 1877. You can read details in this blog post of mine: https://blogs.ams.org/visualinsight/2016/06/15/small-stellated-dodecahedron/ … (7/n, n = 7)pic.twitter.com/0p97aKGfa3
Fun Fact: You can use the 4 holes to encode 8 qubits ! :) https://arxiv.org/abs/1712.07666
Cool! I'll check it out.
Here's a 6-colored small stellated dodecahedron (opposite colors the same). It suggests a 6-coloring for the {5,5} tiling, although hard to see when tiles get small so fast.pic.twitter.com/fB70vx8vVO
props on starting the blog with art history! super-cool.
PS link for Constrast: Order and Chaos appears to be broken. Here is a jpeg:pic.twitter.com/FG3jmIi1y5
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