d20.gcode

c1 = 0;                  // coordinate 1
c2 = 1 / 2;              // coordinate 2
c3 = (1 + sqrt(5)) / 4;  // coordinate 3; phi / 2
function icosahedron_faces() = [
  [ 0,  1,  5],  // right rear
  [ 0,  4,  1],  // right front
  [ 0,  5, 10],  // top rear right
  [ 0,  8,  4],  // top front right
  [ 0, 10,  8],  // top right
  [ 1,  4,  9],  // bottom front right
  [ 1,  9, 11],  // bottom right
  [ 1, 11,  5],  // bottom rear right
  [ 2,  3,  6],  // left front
  [ 2,  6,  8],  // top front left
  [ 2,  7,  3],  // left rear
  [ 2,  8, 10],  // top left
  [ 2, 10,  7],  // top rear left
  [ 3,  7, 11],  // bottom rear left
  [ 3,  9,  6],  // bottom front left
  [ 3, 11,  9],  // bottom left
  [ 4,  6,  9],  // front bottom
  [ 4,  8,  6],  // front top
  [ 5,  7, 10],  // rear top
  [ 5, 11,  7],  // rear bottom
];
function icosahedron_vertices() = [
  [ c3,  c1,  c2],  //  0: right top
  [ c3,  c1, -c2],  //  1: right bottom
  [-c3,  c1,  c2],  //  2: left top
  [-c3,  c1, -c2],  //  3: left bottom
  [ c2,  c3,  c1],  //  4: front right
  [ c2, -c3,  c1],  //  5: rear right
  [-c2,  c3,  c1],  //  6: front left
  [-c2, -c3,  c1],  //  7: rear left
  [ c1,  c2,  c3],  //  8: top front
  [ c1,  c2, -c3],  //  9: bottom front
  [ c1, -c2,  c3],  // 10: top rear
  [ c1, -c2, -c3],  // 11: bottom rear
];
module icosahedron(size) {
  scale(size) polyhedron(icosahedron_vertices(), icosahedron_faces());
}
function normal_x(tri) = 
  (tri[1][0]-tri[0][0]) * (tri[2][2]-tri[0][2])-
  (tri[1][2]-tri[0][2]) * (tri[2][1]-tri[0][1]);
function normal_y(tri) = 
  (tri[1][2]-tri[0][2]) * (tri[2][0]-tri[0][0])- 
  (tri[1][0]-tri[0][0]) * (tri[2][2]-tri[0][2]);
function normal_z(tri) = 
  (tri[1][0]-tri[0][0]) * (tri[2][1]-tri[0][1])-
  (tri[1][1]-tri[0][1]) * (tri[2][0]-tri[0][0]);
function normal(tri) = [normal_x(tri),normal_y(tri),normal_z(tri)];

icosahedron(1);
faces = icosahedron_faces();
vertices = icosahedron_vertices();
a = 360;
for (i = [0:19]) {
  face = [vertices[faces[i][0]],vertices[faces[i][1]],vertices[faces[i][2]]];
  n = normal(face);
  rotate([n[0]*a,n[1]*a,n[2]*a])
    hull() {
      sphere(.1,$fn=20);
      translate([1,0,0])
        sphere(.03,$fn=20);
    }
}