(c24)
(load("astri.mac"),heptag())$

Conway's construction of a regular heptagon, given angle trisection.

Inscribe a star of David in a regular hexagon in a circle, as shown. Draw the line (brown) from the lowermost vertex of the star to a concave vertex next to the uppermost. Draw the "vertical" (magenta) from this concave vertex (say, to the one after the next). Trisect the angle between brown and magenta. The three (black) trisectors meet the horizontal diameter (blue) in three places, at which construct verticals (black) to the circle. The six endpoints of these verticals, plus one endpoint of the diameter, form a regular heptagon.

Note the eyeball indistinguishability between the length of the heptagon side (black, leftmost vertical) = 4 sin pi/7 ~ 1.7355, and the separation of the horizontal sides of the star of David (green and brown) = sqrt 3 = 1.7321