a regular pentagon has what type of symmetry
Pentagon A regular pentagon has five lines of reflectional symmetry, and rotational symmetry of order 5 (through 72째, 144째, 216째 and 288째). 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
Equilateral polygon In geometry, three or more than three straight lines (or segment of a line) make a polygon and  an equilateral polygon is a polygon which has all sides of the same length. Except in the triangle case, it need not be equiangular (need not have all angles equal), but if it does then it is a regular polygon. If the number of sides is at least five, an equilateral polygon need not be a convex polygon: it could be concave or even self-intersecting.