Let M be an orientable hyperbolic surface without boundary and let $\gamma$ be a closed geodesic in M. We prove that any side of any triangle formed by distinct lifts of $\gamma$ in H2 is shorter than $\gamma$.
Regular tessellations of the hyperbolic plane by fundamental domains of a Fuchsian group
Computation in word-hyperbolic groups
The exceptional simple Lie group $F_{4(-20)}$, after J. Tits
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