The math is easy. the formula for an octagon from a square is:
L – {L(.2071)2}/2
Where L is the length of the side of the square and .2071 is constant. You can simplify the formula if you break it into two pieces:
L(.2071)2 = LO
Where LO is the length of the octagon side. Plug that into the formula above and you get:
L-LO/2
tells you how far from each corner of the square to set the posts.
Example for this gazebo:
L=144"
144" – {144"*.2071*2}/2 = 42.1776"
or
144*.2071*2 = 59.6448 (length of the side of the octagon LO)
144-59.6448/2 = 42.1776
Don’t bother trying to measure out to 4 decimal places LOL! Just round it to two or three places and convert to a fraction.
If you want to skip ahead and see the finished product I posted a picture of it here
Where are the band-aids?---Pro Libertate!