# Question #7ba0a

There are infinitely many choices. See below for a case involving $16$ sides.
Think of a regular octagon where you cut an isosceles triangle from each corner and form a $16$-gon. If all the triangles are congruent and they are not exactly the right size, you end up with alternating longer and shorter sides. But, because all angles in the cut $16$-gon are still congruent and alternating sides are congruent too, a ${45}^{\circ}$ rotation gives back the same polygon just as it did for the regular octagon.