Hyperbolic isometry
| If the two reflecting lines are parallel the
parabolic isometry is the composition of two reflections in these
lines.
A vertex of the triangle and its corresponding image lie on a horocycle at the point on the boundary where the parallel lines meet and through the vertex. This isometry is equivalent to a translation in the Euclidean plane. |
Elliptic isometry
Hyperbolic isometry
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