How are rotations DIFFERENT from translations and reflections?

Answer 1

All three are actions of symmetry.When translation (shift on a specific distance) acts on a symmetric pattern like IIIIIIIIII written to infinity or on a closed surface the pattern is unchanged. Reflection is a flip (turn around the mirror line) like b I d this two letter word has a mirror symmetry. Letters A V M Y have a vertical reflection. Letters D B have horizontal. Letters X H O have both vertical and horizontal.

Rotation is another action that leaves a symmetric object unchanged. Letters H has symmetry of rotation 180 and 360 degrees (two rotations) same as Z S but the former has also line symmetry (two rotations and two lines always the same number for both due to Leonardo DaVincci) and the latter only rotations (two).

The infinite number of rotations has a circle.