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
- 01
The shape is a kite. Rotational symmetry asks how it looks while you turn it about its center — not how it folds.
- 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.
- 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.