<P> If squares are constructed all internally or all externally on the sides of an octagon, then the midpoints of the segments connecting the centers of opposite squares form a quadrilateral that is both equidiagonal and orthodiagonal (that is, whose diagonals are equal in length and at right angles to each other). </P> <P> The midpoint octagon of a reference octagon has its eight vertices at the midpoints of the sides of the reference octagon . If squares are constructed all internally or all externally on the sides of the midpoint octagon, then the midpoints of the segments connecting the centers of opposite squares themselves form the vertices of a square . </P> <P> A regular octagon is a closed figure with sides of the same length and internal angles of the same size . It has eight lines of reflective symmetry and rotational symmetry of order 8 . A regular octagon is represented by the Schläfli symbol (8). The internal angle at each vertex of a regular octagon is 135 ° (3 π 4 (\ displaystyle \ scriptstyle (\ frac (3 \ pi) (4))) radians). The central angle is 45 ° (π 4 (\ displaystyle \ scriptstyle (\ frac (\ pi) (4))) radians). </P> <P> The area of a regular octagon of side length a is given by </P>

How many lines of symmetry in an octogon