Bi-rotational triangular structure questions

I am trying to model a sculpture that is composed of 6 large triangles. I am trying to position the ground points such that based on those points, the connected panels all rotate to form the figure. I am stuck trying to link the rotation of the triangles to the points.

I’ve attached images of my physical model, I am just lost as to the math behind it! Any help would be appreciated.

Have a gander at some of the kangaroo origami examples