Proper symmetry/Isometry on a geometric object/Definition

Let ${\displaystyle {}T\subseteq V}$ be a subset of a Euclidean vector space. A proper isometry

${\displaystyle f\colon V\longrightarrow V}$

fulfilling ${\displaystyle {}f(T)=T}$ is called a proper symmetry or a motion of ${\displaystyle {}T}$.