Trefoil

The Construction in Details:

How to define the radius Ri of the inner circles:

The radius of all torus tubes is called by R0. Ri is the radius of the inner circles. Ra is the radius of the outer circle.
See the opposite image:
Ri (dark green) = Ra/2 + R0/2.
This increasing by "+ R0/2" is neccesary to get the inner rings ending right above <0,0,0> (marked by the red arrow!). Only in this way the rotated plane (or an according box) can cut off the upper parts right and left from the torus. The opposite image shows the right plane of these two planes used for cut off (transparent yellow).

The inner torus (orange) and
one of the planes used for cut off (yellow)

// outer radius:
#declare Ra = 3.00 -R0;
// radius of inner circles;
#declare Ri  = Ra /2+ R0/2;

#declare Part =
intersection{
torus{ Ri,  R0
       rotate<90,0,0>
       translate<0,-Ra+Ri,0>}
plane { <0,1,0>,0 rotate<0,0, 30>}
plane { <0,1,0>,0 rotate<0,0,-30>}
box{<-Ri-R0,-Ra-R0,-R0>,
     <Ri+R0, 0,R0>}
}// ------- end of "Part" --------
union{   //-----------------------
torus{ Ra,  R0
       rotate<90,0,0>
      } // end of torus  ---------

object{ Part rotate<0,0,0*120>}
object{ Part rotate<0,0,1*120>}
object{ Part rotate<0,0,2*120>}
}// end of union
//---------------------------- end

Click here for the complete scene file for POV-Ray:
".txt" file or ".pov" file