= Right-angled hyperbolic hexagon
A geodesic hexagon in the <hyperbolic plane> with all six interior angles $\pi/2$. Any three positive alternating side lengths determine it up to <isometry>. If those sides are $\ell_i/2$, the opposite seam satisfies $\cosh s_i=(\cosh(\ell_i/2)+\cosh(\ell_j/2)\cosh(\ell_k/2))/(\sinh(\ell_j/2)\sinh(\ell_k/2))$. Two congruent such hexagons glued along the other three sides form a <pair of pants (mathematics)> with boundary lengths $\ell_1,\ell_2,\ell_3$.
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