hi Lionel and Alain,

to follow up, the scene below uses the parametric directly.

Alain's bounding box guess was pretty close (I've added a
frame to show it), I had expected a much smaller object.

----------<snip>----------

// umbilic torus

#version 3.6;

#include "colors.inc"
#include "shapes.inc"

light_source { <100,100,-100> color White }

camera {
  location <0,0,-30>
  look_at <1,-1,0>
}


#declare oUmbilic = parametric {
  function {sin(u)*(7+cos((u/3)-(2*v))+2*cos((u/3)+v))},
  function {cos(u)*(7+cos((u/3)-(2*v))+2*cos((u/3)+v))},
  function {sin((u/3)-(2*v))+2*sin((u/3)+v)}
  <0,0>,<2*pi,2*pi>
  contained_by { box { <-10,-10,-3>, <10,10,3> } }
  accuracy .0001
  precompute 15 x,y,z
}


union {

  object { oUmbilic pigment { Blue } }

  object {
    Wire_Box_Union(<-10.1,-10.1,-3.1>,<10.1,10.1,3.1>,.05)
    pigment { Red }
  }

  rotate -z*15
  rotate x*30
  rotate y*clock*360
}

----------<snip>----------

thank you both.

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