// scalloped knob
  
diameter = 30; // very rough overall diameter
s = 6;         // number of scallops


///////////

d=diameter/(s);
 
$fn=100;

//offset = d*2.3; // for s=4
//md=3; // for s=4

//offset = d*2.68; // for s=4
//md=3.7; // for s=4

//offset=d*3.05;// for s=5
//md=4.5; // for s=5

//offset = d*3.4; //for s=6
//md=5.3 ;//for s=6

//offset = d*3.75; //for s=7
//md=5.8 ;//for s=7

//offset = d*4.09; //for s=8
//md=6.6 ;//for s=8

//offset=d*4.42; // for s=9
//md= 7.25; // for s=5


// formula calculated by chatgpt
offset = -0.0043 * s * s + 0.4034 * s + 1.1363;
md = -0.0134 * s * s + 0.8755 * s + 0.4389;

echo(offset,md);

// basic shape generation

module profile(){
  difference(){
    union(){
      rotate([0,0,360/(s*2)])
        for (j = [0 : 360 / s : 360]) {
            rotate([0, 0, j])
            translate([s * d  / PI, 0, 0])
            circle(d = d * 2); 
        }
     circle(d=md*d);
    }         
        for (j = [0 : 360 / s : 360]) {   
            rotate([0, 0, j])
            translate([offset*d,0,0])
            circle(d = d * 2); 
       }   
  }  
}

profile();  

//linear extrude and round off (or chamfer)