Some articles on isometries:

Euclidean Plane Isometry - Isometries in The Complex Plane
... In terms of complex numbers, the isometries of the plane either of the form or of the form for some complex numbers a and ω with
Point Groups In Three Dimensions - Group Structure
... SO(3) is a subgroup of E+(3), which consists of direct isometries, i.e ... isometries preserving orientation it contains those that leave the origin fixed ... −I } Thus there is a 1-to-1 correspondence between all direct isometries and all indirect isometries, through inversion ...
Hyperboloid Model - Isometries
... In a different language, it is the group of linear isometries of the Minkowski space ... space of rank 1, In fact, the group SO+(1,n) is the full group of orientation-preserving isometries of the n-dimensional hyperbolic space ...