I am having visions of a soft fruit basket of cotton yarn. It would have a square bottom and an octagon top. Well, maybe more of an octagon middle since by the top it might be quite circular unless given a bit of wire or something to keep the corners.
The plan, I think, starts with choosing a finished circumference in stitches that is an odd number time eight. The knitting would start with the same squares as before for the bottom. When the number of stitches is half the planned complete number, stop increasing on half of the increases while the others start increasing to the other side. I've been thinking that the increases should center around opposing sides, but perhaps on the same side of each edge would be better. And the more I ponder which is better the more I think it won't really hit an octagon shape at all. The first will go more to a boat shape and the second will continue to be square but will twist a bit as it goes. It really doesn't even need to have the increases change sides.
For a more rounded project, one could start a little earlier in the shaping and just decrease the frequency of increases along the lines that will be stopped. Patterning could be used to emphasis or even generate the octagonal shape, if that is desired...
It's a work in progress, of course, until something has been knit. And then there's always the second one.
