[ogdaoqmc] square to octagon to hexadecagon

start with a unit square.  measure 1-sqrt(0.5) ~= 0.293 from each corner along each edge, and cut off the corners.  this results in a regular octagon with side length tan(pi/8) = sqrt(2)-1 ~= 0.414 .

measure in from each octagon vertex sqrt(2)-sqrt(1+sqrt(0.5)) ~= 0.108 and cut corners again to yield a 16-gon (hexakaidecagon) with side length tan(pi/16) = sqrt(4+sqrt(8)) - sqrt(2) - 1 ~= 0.199 .

the distance between opposite edges remains 1.

previously, hexagon.