Octagonal Tower Proportions

[Athos]

I'm working on a octagonal tower using hinge bricks and plates. I thought I had it right, but when I went to put the roof on, it turned out the proportions must be slightly off. And, I don't feel like doing trying to sort out the math especially with the complication of the hinges.

So I thought I'd ask here. If want the walls to be 10 studs long. How wide does it need to be?

Steve

[jimmynick]

~26.14 studs, but the distance from the centre to the corner will be a smidge longer.