Rotational symmetry

The question

How many times does it land on itself?

How it works.

kite
lands on itselfonly at the full turn
order=1
  1. 01

    The shape is a kite. Rotational symmetry asks how it looks while you turn it about its center — not how it folds.

  2. 02

    Its two pairs of equal sides are next to each other rather than opposite, so a turn would have to carry a long side onto a short one. Nothing short of a whole turn works. It folds in half down the middle, but folding is not turning.

  3. 03

    So only the full turn brings it back, which is what order 1 means: the shape lands on itself once in a complete turn.