use <utils.scad>

module d4(size=false, side=false) {
    l = side ? side : s2s_d4(size);
    if (l == false) {
        echo("ERROR: d4: one of side or size should be defined");
    }
    r = sqrt(6)/4*l;
    c = r*2;
    difference() {
        intersection() {
            sphere(r=r*0.79, $fn=64);
            translate([0, 0, r-r/3]) cube(c, center=true);
            intersection_for ( i = [0:2] ) {
                rotate([0, 0, 120*i]) rotate([acos(1/3)+180, 0, 0]) 
                    translate([0, 0, r-r/3]) cube(c, center=true);
            }
        }
        rotate([180, 0, 0]) translate([0, 0, r/3]) child(0);
        rotate([acos(1/3)+180, 0, 0]) rotate([180, 0, 0]) translate([0, 0, r/3]) child(1);
        rotate([0, 0, 120]) rotate([acos(1/3)+180, 0, 0]) rotate([180, 0, 0]) translate([0, 0, r/3]) child(2);
        rotate([0, 0, 240]) rotate([acos(1/3)+180, 0, 0]) rotate([180, 0, 0]) translate([0, 0, r/3]) child(3);
    }
}

module d6(size=false, side=false) {
    l = side ? side : s2s_d6(size);
    if (l == false) {
        echo("ERROR: d6: one of side or size should be defined");
    }
    difference() {
        intersection() {
            cube(l, center=true);
            sphere(l*0.79);
        }
        translate([0, 0, l/2]) child(0);
        rotate([90, 0, 0]) translate([0, 0, l/2]) child(1);
        rotate([0, 90, 0]) translate([0, 0, l/2]) child(2);
        rotate([-90, 0, 0]) translate([0, 0, l/2]) child(3);
        rotate([0, -90, 0]) translate([0, 0, l/2]) child(4);
        rotate([180, 0, 0]) translate([0, 0, l/2]) child(5);
    }
}

module d8(size=false, side=false) {
    l = side ? side : s2s_d8(size);
    if (l == false) {
        echo("ERROR: d8: one of side or size should be defined");
    }
    r = sqrt(2)/2*l;
    c = r*2;
    i_r = sqrt(6)/6*l;
    difference() {
        intersection() {
            sphere(r*0.86, $fn=64);
            cube([c, c, i_r*2], center=true);
            intersection_for ( i = [0:2] ) {

                rotate([0, 0, 120*i]) rotate([acos(-1/3), 0, 0]) cube([c, c, i_r*2], center=true);
            }
        }
        translate([0, 0, i_r]) child(0);
        rotate([acos(-1/3), 0, 0]) translate([0, 0, i_r]) child(1);
        rotate([0, 0, 120]) rotate([acos(-1/3)+180, 0, 0]) translate([0, 0, i_r]) child(2);
        rotate([0, 0, -120]) rotate([acos(-1/3)+180, 0, 0]) translate([0, 0, i_r]) child(3);
        rotate([0, 0, -120]) rotate([acos(-1/3), 0, 0]) translate([0, 0, i_r]) child(4);
        rotate([0, 0, 120]) rotate([acos(-1/3), 0, 0]) translate([0, 0, i_r]) child(5);
        rotate([acos(-1/3)+180, 0, 0]) translate([0, 0, i_r]) child(6);
        rotate([180, 0, 0]) translate([0, 0, i_r]) child(0);
    }
}

module d12(size=false, side=false) {
    l = side ? side : s2s_d12(size);
    if (l == false) {
        echo("ERROR: d12: one of side or size should be defined");
    }
    r = l*sqrt(3)*(1+sqrt(5))/4;
    c = r*2;
    i_r = (l/2)*sqrt(5/2 + 11*sqrt(5)/10);
    difference() {
        intersection() {
            sphere(r*0.96, $fn=64);
            cube([c, c, i_r*2], center=true);
            intersection_for ( i = [0:4] ) {

                rotate([0, 0, 72*i]) rotate([acos(-1/sqrt(5)), 0, 0]) cube([c, c, i_r*2], center=true);
            }
        }
        translate([0, 0, i_r]) child(0);
        rotate([acos(-1/sqrt(5))+180, 0, 0]) translate([0, 0, i_r]) child(1);
        rotate([0, 0, 72]) rotate([acos(-1/sqrt(5))+180, 0, 0]) translate([0, 0, i_r]) child(3);
        rotate([0, 0, 144]) rotate([acos(-1/sqrt(5))+180, 0, 0]) translate([0, 0, i_r]) child(5);
        rotate([0, 0, 216]) rotate([acos(-1/sqrt(5))+180, 0, 0]) translate([0, 0, i_r]) child(4);
        rotate([0, 0, 288]) rotate([acos(-1/sqrt(5))+180, 0, 0]) translate([0, 0, i_r]) child(2);

        rotate([acos(-1/sqrt(5)), 0, 0]) translate([0, 0, i_r]) child(10);
        rotate([0, 0, 72]) rotate([acos(-1/sqrt(5)), 0, 0]) translate([0, 0, i_r]) child(8);
        rotate([0, 0, 144]) rotate([acos(-1/sqrt(5)), 0, 0]) translate([0, 0, i_r]) child(6);
        rotate([0, 0, 216]) rotate([acos(-1/sqrt(5)), 0, 0]) translate([0, 0, i_r]) child(7);
        rotate([0, 0, 288]) rotate([acos(-1/sqrt(5)), 0, 0]) translate([0, 0, i_r]) child(9);
        rotate([180, 0, 0]) translate([0, 0, i_r]) child(11);
    }
}

module d20(size=false, side=false) {
    l = side ? side : s2s_d20(size);
    if (l == false) {
        echo("ERROR: d20: one of side or size should be defined");
    }
    sc_face = 0.5;
    r = l*sqrt(10+2*sqrt(5))/4;
    c = r*2;
    i_r = (l/12)*sqrt(3)*(3+sqrt(5));
    a_b2 = atan(1/2) + acos(-sqrt(5)/3)/2;
    phi = (1+sqrt(5))/2;
    rotate([0, -acos((-(1+sqrt(5)))/(2*sqrt(3))), 0]) 
    difference() {
        intersection() {
            sphere(r*0.96, $fn=64);
            rotate([0, acos((-(1+sqrt(5)))/(2*sqrt(3))), 0]) cube([c, c, i_r*2], center=true);
            mirror([1, 0, 0]) rotate([0, acos((-(1+sqrt(5)))/(2*sqrt(3))), 0]) cube([c, c, i_r*2], center=true);
            rotate([0, acos(1/sqrt(3)), -45]) cube([c, c, i_r*2], center=true);
            mirror([1, 0, 0]) rotate([0, acos(1/sqrt(3)), -45]) cube([c, c, i_r*2], center=true);
            mirror([0, 1, 0]) rotate([0, acos(1/sqrt(3)), -45]) cube([c, c, i_r*2], center=true);
            mirror([0, 1, 0]) mirror([1, 0, 0]) rotate([0, acos(1/sqrt(3)), -45]) cube([c, c, i_r*2], center=true);
            rotate([90, 0, 0]) rotate([0, acos((sqrt(5)+1)/(2*sqrt(3))), 90]) cube([c, c, i_r*2], center=true);
            mirror([0, 0, 1]) rotate([90, 0, 0]) rotate([0, acos((sqrt(5)+1)/(2*sqrt(3))), 90]) cube([c, c, i_r*2], center=true);
            rotate([0, 90, atan((-sqrt(5)+1)/(sqrt(5)+1))]) cube([c, c, i_r*2], center=true);
            mirror([0, 1, 0]) rotate([0, 90, atan((-sqrt(5)+1)/(sqrt(5)+1))]) cube([c, c, i_r*2], center=true);
        }
        rotate([0, acos((-(1+sqrt(5)))/(2*sqrt(3))), 0]) translate([0, 0, i_r]) rotate([0, 0, 90]) scale([sc_face, sc_face, 1]) child(0);
        rotate([180, acos((-(1+sqrt(5)))/(2*sqrt(3))), 0]) translate([0, 0, i_r]) rotate([0, 0, 270]) scale([sc_face, sc_face, 1]) child(19);

         mirror([1, 0, 0]) rotate([0, acos((-(1+sqrt(5)))/(2*sqrt(3))), 0]) translate([0, 0, i_r]) mirror([0, 1, 0]) rotate([0, 0, 90]) scale([sc_face, sc_face, 1]) child(12);
         mirror([1, 0, 0]) rotate([180, acos((-(1+sqrt(5)))/(2*sqrt(3))), 0]) translate([0, 0, i_r]) mirror([0, 1, 0]) rotate([0, 0, 90]) scale([sc_face, sc_face, 1]) child(7);

         rotate([0, acos(1/sqrt(3)), -45]) translate([0, 0, i_r]) scale([sc_face, sc_face, 1]) child(9);
         rotate([180, acos(1/sqrt(3)), -45]) translate([0, 0, i_r]) scale([sc_face, sc_face, 1]) child(10);

         mirror([1, 0, 0]) rotate([0, acos(1/sqrt(3)), -45]) translate([0, 0, i_r]) mirror([1, 0, 0]) scale([sc_face, sc_face, 1]) child(1);
         mirror([1, 0, 0]) rotate([180, acos(1/sqrt(3)), -45]) translate([0, 0, i_r]) mirror([1, 0, 0]) scale([sc_face, sc_face, 1]) child(18);

         mirror([0, 1, 0]) rotate([0, acos(1/sqrt(3)), -45]) translate([0, 0, i_r]) mirror([0, 1, 0]) rotate([0, 0, 180]) scale([sc_face, sc_face, 1]) child(15);
         mirror([0, 1, 0]) rotate([180, acos(1/sqrt(3)), -45]) translate([0, 0, i_r]) mirror([0, 1, 0]) rotate([0, 0, 180]) scale([sc_face, sc_face, 1]) child(4);

         mirror([0, 1, 0]) mirror([1, 0, 0]) rotate([0, acos(1/sqrt(3)), -45])  translate([0, 0, i_r]) mirror([0, 1, 0]) mirror([0, 1, 0]) scale([sc_face, sc_face, 1]) child(13);
         mirror([0, 1, 0]) mirror([1, 0, 0]) rotate([180, acos(1/sqrt(3)), -45])  translate([0, 0, i_r]) mirror([0, 1, 0]) mirror([0, 1, 0]) scale([sc_face, sc_face, 1]) child(6);

         rotate([90, 0, 0]) rotate([0, acos((sqrt(5)+1)/(2*sqrt(3))), 90]) translate([0, 0, i_r]) rotate([0, 0, 270]) scale([sc_face, sc_face, 1]) child(11);
         rotate([270, 0, 0]) rotate([0, acos((sqrt(5)+1)/(2*sqrt(3))), 90]) translate([0, 0, i_r]) rotate([0, 0, 270]) scale([sc_face, sc_face, 1]) child(8);

         mirror([0, 0, 1]) rotate([90, 0, 0]) rotate([0, acos((sqrt(5)+1)/(2*sqrt(3))), 90]) translate([0, 0, i_r]) mirror([1, 0, 0]) rotate([0, 0, 90]) scale([sc_face, sc_face, 1]) child(14);
         mirror([0, 0, 1]) rotate([270, 0, 0]) rotate([0, acos((sqrt(5)+1)/(2*sqrt(3))), 90]) translate([0, 0, i_r]) mirror([1, 0, 0]) rotate([0, 0, 90]) scale([sc_face, sc_face, 1]) child(5);

         rotate([0, 90, atan((-sqrt(5)+1)/(sqrt(5)+1))]) translate([0, 0, i_r]) rotate([0, 0, 180]) scale([sc_face, sc_face, 1]) child(16);
         rotate([180, 90, atan((-sqrt(5)+1)/(sqrt(5)+1))]) translate([0, 0, i_r]) rotate([0, 0, 180]) scale([sc_face, sc_face, 1]) child(3);

         mirror([0, 1, 0]) rotate([0, 90, atan((-sqrt(5)+1)/(sqrt(5)+1))]) translate([0, 0, i_r]) mirror([0, 1, 0]) scale([sc_face, sc_face, 1]) child(2);
         mirror([0, 1, 0]) rotate([180, 90, atan((-sqrt(5)+1)/(sqrt(5)+1))]) translate([0, 0, i_r]) mirror([0, 1, 0]) scale([sc_face, sc_face, 1]) child(17);
    }
}