This question, sent in on a postcard of the front at Weston-super-Mare, the signature, perhaps ‘W’, washed out by the bracing spray of the sea, is surprisingly far-reaching.
Of course you can cut an Octagon in half in innumerable ways, but only two methods will give you symmetrical halves: first a cut from a corner on one side to the corner opposite, and second a cut from midway down one of the sides to the opposite side. The latter was almost invariably preferred because the half-octagon then gave a broadly rectangular building of proportions 1:2 but with dropped corners. I hope that answers the question, but it leads one to ask why octagons were more popular than other ground plans. It may be helpful for our correspondent to look at 18th century optical theory.
The question of what one could see, and how one saw, from a fixed point was discussed by William Porterfield and Hogarth. The average landscape painting by Claude has a 30o compass, and an Octagon is constructed with 45o angles from its centre. If up to 15o are likely to be taken up with the structure that supports the roof, then there is a natural fit between an octagonal structure and a composed view. One might go on to suggest that views from Octagons are so often divided into three for a similar reason – we can just about take in 135o in a single glance.