<P> A pentagon may be simple or self - intersecting . A self - intersecting regular pentagon (or star pentagon) is called a pentagram . </P> <P> A regular pentagon has Schläfli symbol (5) and interior angles are 108 ° . </P> <P> A regular pentagon has five lines of reflectional symmetry, and rotational symmetry of order 5 (through 72 °, 144 °, 216 ° and 288 °). The diagonals of a convex regular pentagon are in the golden ratio to its sides . Its height (distance from one side to the opposite vertex) and width (distance between two farthest separated points, which equals the diagonal length) are given by </P> <Dl> <Dd> Height = 5 + 2 5 2 ⋅ Side ≈ 1.539 ⋅ Side, (\ displaystyle (\ text (Height)) = (\ frac (\ sqrt (5 + 2 (\ sqrt (5)))) (2)) \ cdot (\ text (Side)) \ approx 1.539 \ cdot (\ text (Side)),) </Dd> <Dd> Width = Diagonal = 1 + 5 2 ⋅ Side ≈ 1.618 ⋅ Side, (\ displaystyle (\ text (Width)) = (\ text (Diagonal)) = (\ frac (1 + (\ sqrt (5))) (2)) \ cdot (\ text (Side)) \ approx 1.618 \ cdot (\ text (Side)),) </Dd> <Dd> Diagonal = R 5 + 5 2 = 2 R cos ⁡ 18 ∘ = 2 R cos ⁡ π 10 ≈ 1.902 R, (\ displaystyle (\ text (Diagonal)) = R \ (\ sqrt (\ frac (5 + (\ sqrt (5))) (2))) = 2R \ cos 18 ^ (\ circ) = 2R \ cos (\ frac (\ pi) (10)) \ approx 1.902 R,) </Dd> </Dl>

A regular pentagon has what type of symmetry