But note that the Discordian "mandala" is not actually Brunnian. An easy way to see that is to look at the folllowing sublink and notice that yellow lies atop red, which lies atop green, which lies atop yellow, etc., so these three are the Borromean rings (and are thus linked, which must not be the case if the original link is Brunnian).

My situation is that every loop plays the same role, if I undo any loop all will become undone!

Exactly that is the case: If one removes the red link, the other 4 links are free, this is obvious and you have seen it too.

But what happens, if one removes the most inner (the cyan) rectangular link? Now one can weave out the read one (do it in your mind) and the other three are then free. The same holds for every of the rectangular links. So they have all the same topological quality.

Do a redraw of a redraw of a redraw

(* Take 5 from http://katlas.org/wiki/File:6Loops-Brunnian-link.png *) 
Graphics3D[{{Yellow, Specularity[White, 70], 
   Tube[{{0, 12, 0}, {23, 12, 0}, {23, -12, 0}, {0, -12, 0}, {0, 12, 
      0}}, 1/3]},
  {Green, Specularity[White, 70], 
   Tube[{{1, 9, 0}, {22, 9, 0}, {22, -9, 0}, {1, -9, 0}, {1, 9, 0}}, 
    1/3]},
  {Blue, Specularity[White, 70], 
   Tube[{{2, 6, 0}, {21, 6, 0}, {21, -6, 0}, {2, -6, 0}, {2, 6, 0}}, 
    1/3]},
  {Cyan, Specularity[White, 70], 
   Tube[{{3, 3, 0}, {20, 3, 0}, {20, -3, 0}, {3, -3, 0}, {3, 3, 0}}, 
    1/3]},
  {Red, Specularity[White, 40], 
   Tube[BSplineCurve[{{23/2, 2, 0}, {19, 2, 0}, (* 
      über 1 *) {19, -3, 2},
      (* über 2, 3, 
      4 *) {19, -6, 2}, {19, -9, 2}, {19, -12, 2}, {19, -15, 0},
      (* unter 4, über 3 *) {18, -15, 0}, {18, -12, -2}, {18, -9, 2},
      (* unter 3, 
      unter 4 *) {18, -15/2, 0}, {17, -15/2, 
       0}, {17, -9, -2}, {17, -12, -2}, {17, -15, 0},
      (* über 4, unter 3, 
      über 2 *) {16, -15, 0}, {16, -12, 2}, {16, -9, -2}, {16, -6, 
       2}, {16, -9/2, 0}, {15, -9/2, 0},
      (* unter 2, unter 3, 
      über 4 *) {15, -6, -2}, {15, -9, -2}, {15, -12, 2}, {15, -15, 
       0}, {14, -15, 0},
      (* unter 4, 
      unter 3 *) {14, -12, -2}, {14, -9, -2}, {14, -15/2, 
       0}, {13, -15/2, 0},
      (* über 3, 
      unter 4 *) {13, -9, 2}, {13, -12, -2}, {13, -15, 0}, {12, -15, 
       0},
      (* über 4, über 3, unter 2, 
      über 1 *) {12, -12, 2}, {12, -9, 2}, {12, -6, -2}, {12, -3, 
       2}, {12, -3/2, 0}, {11, -3/2, 0},
      (* unter 1, unter 2, über 3, 
      über 4 *) {11, -3, -2}, {11, -6, -2}, {11, -9, 2}, {11, -12, 
       2}, {11, -15, 0}, {10, -15, 0},
      (* unter 4, 
      über 3 *){10, -12, -2}, {10, -9, 2}, {10, -15/2, 0}, {9, -15/2, 
       0},
      (* unter 3, 
      unter 4 *) {9, -9, -2}, {9, -12, -2}, {9, -15, 0}, {8, -15, 0},
      (* über 4, unter 3, 
      unter 2 *){8, -12, 2}, {8, -9, -2}, {8, -6, -2}, {8, -9/2, 
       0}, {7, -9/2, 0},
      (* über 2,unter 3, 
      über 4 *) {7, -6, 2}, {7, -9, -2}, {7, -12, 2}, {7, -15, 
       0}, {6, -15, 0},
      (* unter 4, 
      unter 3 *) {6, -12, -2}, {6, -9, -2}, {6, -15/2, 0}, {5, -15/2, 
       0},
      (* über 3, 
      unter 4 *) {5, -9, 2}, {5, -12, -2}, {5, -15, 0}, {4, -15, 0},
      (* über 4,über 3, über 2, 
      unter 1 *) {4, -12, 2}, {4, -9, 2}, {4, -6, 2}, {4, -3, -2}, {4,
        2, 2}, {23/2, 2, 0}
      }], 1/3]}
  }, ViewPoint -> Top, BoxRatios -> Automatic, Background -> Black, 
 Boxed -> False]

Hi Krause .Yes that is (Mandala) what I am using (I googled it) but my question is how to get Mathematica to draw the links so that I am able to change some parameters and alter the shape

So basically the model is not mathematically defined

So it's not a model but rather a description. Let's try it again: Is the following (see Borromean Rings) the intended representation to your description?

Something like this

this one

... serves as an illustration of a symmetric Brunnian link of order 5.

So do you have a model of a Brunnian 5 link?