Solve the above problem using this hint: 1. Consider the properties of a regular octagon, how many lines of symmetry does a regular octagon have and what happens when you rotate a shape and overlap it with itself. 2. For the rotation, the angle of rotation is $\frac{\pi}{8}8\pi (22.5 \degree)$ for which the pattern is repeated 8 times. Through this information, calculate the total angle covered by all rotations. 3. For finding the lines of symmetry, consider where the lines of symmetry will occur (i.e., through the vertices of the overlapped octagon and through the midpoints of the overlapped sides). 4. Use the fact that, when shapes overlap with regular rotations, the resulting figure often has more lines of symmetry than the original shape