Triangle group
= Triangle group
{title2=$\Delta(p,q,r)$}
{wiki}
A <triangle group> is generated by <reflections> in the sides of a triangular <fundamental domain> in <spherical geometry>, <Euclidean geometry> or <hyperbolic geometry>. The angles $\pi/p,\pi/q,\pi/r$ determine the geometry through the sign of $1/p+1/q+1/r-1$. Its orientation-preserving <subgroup> has <group presentation> $\langle x,y,z\mid x^p=y^q=z^r=xyz=1\rangle$.