The vertices of a regular polygon are equally spaced around its centre. Moving every vertex to the next gives a matching position.

There are \(n\) such equal steps in a full turn, so each is \(\displaystyle \frac{360^\circ}{n}\) and the order is \(n\).

Answer

Rotational order \(n\); smallest matching turn \(\displaystyle \frac{360^\circ}{n}\).