A line of symmetry reflects a figure onto itself. Rotational symmetry of order \(k\) means that the figure matches itself \(k\) times in a full turn, including the starting position at \(360^\circ\). Its smallest positive matching turn is \(\dfrac{360^\circ}{k}\).

A regular octagon matches itself after each \(45^\circ\) turn. It has 8 symmetry lines: 4 through opposite vertices and 4 through midpoints of opposite sides. A non-square rectangle has order 2, not 4, because a \(90^\circ\) turn exchanges unequal side lengths.

Reflection and rotational symmetry

Reflection and rotational symmetry

Figure	Lines of symmetry	Rotational order
Regular pentagon / hexagon / octagon / decagon	5 / 6 / 8 / 10	5 / 6 / 8 / 10
Equilateral triangle	3	3
Isosceles triangle, not equilateral	1	1
Rectangle, not square	2	2
Rhombus, not square	2 (its diagonals)	2
Square	4	4
Parallelogram, neither rectangle nor rhombus	0	2
Kite, not a rhombus	1	1
Isosceles trapezium	1	1