Klein quartic
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In hyperbolic geometry, the Klein quartic, named after Felix Klein, is a compact Riemann surface of genus 3 with the highest possible order automorphism group for this genus, namely order 168 orientat
The Eightfold Way – sculpture by Helaman Ferguson and accompanying book.
Systolic geometry
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In mathematics, systolic geometry is the study of systolic invariants of manifolds and polyhedra, as initially conceived by Charles Loewner and developed by Mikhail Gromov, Michael Freedman, Peter Sar
Klein quartic
…elements in 1 + I Q H u r . The least absolute value of a trace of a hyperbolic element in Γ(I) is η 2 + 3 η + 2 , corresponding the value 3.936 for the systole of the Klein quartic, one of the highest in this genus. The Klein quartic admits tilings connected with the symmetry group (a "regular map"), and these…
A geodesic on a football illustrating the proof of Gromov's filling area conjecture in the hyperelliptic case (see explanation below).