It is fast. It only took 3s to render on my fx-8350 computer.

#declare height = 0.5;
#declare poly_n = 6;
#declare poly_r = 0.5;
#declare cycle_r = 0.13;
#declare an = 2*pi/poly_n;
#declare poly_thr = poly_r*cos(an/2);
#declare bound=max(cycle_r,poly_r);
#declare multi = 1000;

#declare poly_obj =
polynomial{
4,
xyz(0,2,2):multi*1,
xyz(2,0,1):multi*2*height,
xyz(1,0,2):multi*2*(poly_thr-cycle_r),
xyz(2,0,0):multi*(-pow(height, 2)),
xyz(0,0,2):multi*(-pow(cycle_r - poly_thr, 2)),
xyz(1,0,1):multi*2*height*(-2*poly_thr + cycle_r),
xyz(1,0,0):multi*2*pow(height,2)*poly_thr,
xyz(0,0,1):multi*2*height*poly_thr*(poly_thr - cycle_r),
xyz(0,0,0):multi*(-pow(poly_thr*height, 2))
sturm
}

#declare mockup2 =
difference{
    cylinder{
    <0,0,0.0>,<0,0,height>, bound
    }

    #for(i, 0, poly_n-1)
        object{
        poly_obj
        inverse
        rotate <0,0,degrees(an*i)>
        }
        plane{
        <1,0,0>,-poly_thr
        rotate <0,0,degrees(an*i)>
        }
    #end
}

mockup2

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