§ Vyn's feeling about symmetry

• They are of the opinion that the correct definition of a symmetry of an object $S$ in space is that a transformation $T$ is a symmetry of $S$ iff $T(S) = S$ (as a set).
• The above rules out things like translations of a cube.
• Indeed, one can only recover translations by considering a line on the space and then considering the orbit of the line under a specific translation $T$.