Drawing an N-gon around a circle using OpenSCAD

n-gon_around_circle.scad

/*
  Drawing an N-gon around a circle using OpenSCAD
  https://gist.github.com/xunker/daabf70dbb8e990077d3a1a11d1e06dd

  Matthew Nielsen - github.com/xunker

  Math credit: http://mathcentral.uregina.ca/QQ/database/QQ.09.06/s/cliff1.html
*/

/* Diameter of the circle around which the n-gon will be built. */
circle_d = 21.6;  // 21.6mm is 3/4 inch.

/* Number of sides the n-gon should have. Needs to be 3 or more, or else it's
   not a polygon anymore. */
sides = 8;

/* -- no more changes needed below this -- */

circle_r = circle_d/2;
theta = 360 / (sides*2); // sides*2 because each section has two radians to centre.

side_length = (circle_r*2)*tan(theta);

side_angle = theta*2;

%cylinder(h=1, d=circle_d, $fn=32, center=true);

for (angle = [0:side_angle:359]) {
  rotate([0,0,angle])
    translate([0,circle_d/2,0])
      cube([side_length,0.1,1], center=true);
}

n-gon_around_circle.stl