That was where my original solution ended, however following feedback after the puzzle went live on Friday, it isn’t necessarily clear that three equally spaced segments have a constant combined sum, so I have added proof of that. Since the edge length of the 24-gon is the same we only need to consider the perpendicular distance to the internal point. Since this three segments are equally spaced, if we extended the bases we would form an equilateral triangle, making it equivalent to the situation illustrated below.