Okay, this is finally the last time I try it too using what you had done
here before Paul  :-)
  With AA done on it and looking face on it seems fine, plus it's
now complete with that pair of dots found on these symbols.  What I still
don't know though is which is Ying and which is Yang, so switch the names if
need be.
  Tweaking, if any, left up to others from now on.

// Ying Yang again
camera {location < 0, 5, 0 >look_at 0}
light_source {10*y,1}

background {color rgb <1,0,0>}

#declare O_Ying=
intersection
{
 cylinder
 {
  < 0,-0.199, 0>, < 0, 0.199, 0>, 2
 }
 box
 {
  <-3,-0.2,-3>, < 3, 0.2, 0>
  inverse
 pigment {rgb <1,0,0>}
 }
 cylinder
 {
  <-1,-0.2, 0>, <-1, 0.2, 0>, 1
  inverse
 }
}

#declare O_Yang=
union
{
 object
 {
  O_Ying
 }
 cylinder
 {
  < .975,-0.2, 0>, < .975, 0.2, 0>, .975
 }
 cylinder // the white sides (black) dot
 {
  < .975,-0.21, 0>, < .975, 0.21, 0>, .25
   pigment {rgb 0}
 }
  rotate 180*y
}

#declare YingYang=
union {
union {
object {O_Ying}
 cylinder
 {
  <.975,-0.2, 0>, <.975, 0.2, 0>, .975
 }
 cylinder // the black sides (white) dot
 {
  < .975,-0.21, 0>, < .975, 0.21, 0>, .25
   pigment {rgb 1} finish {ambient 1}
 }
 pigment {rgb 0}
}

object {O_Yang pigment {rgb 1} finish {ambient 1}}
}

YingYang

// Bob

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