Question: How do I model a molecule?

I would like to model the kinematics of a collection of points in R^3 - which represent atoms  on a molecule - using Maple. I want to specify the fixed distances between the points.  I just saw a formula in a book I own for the number of degrees of freedom of such a system. I wil have plenty of degrees of freedom with which to work. So, I will begin - in the simplest case - by arbitrarily specifying as many of the coordinates for the points as possible.

Does anyone have an idea of how best to program such a model?

I tried something like

x[1]:=0; y[1]:=0; z[1]:=0;

x[2]:=a2; y[2]:=0; z[2]:=0; // point P2

x[3]:=a3; y[3]:=b3; z[3]:=0; // point P3

with a2, a3, b3 arbitrary. Then, I want to specify a4, b4, c4 in such a way that the distance between point 3 and P2 is given by d23.

This will leave 2 of a4, b4, c4 arbitrary. Ideally, then, I want to specify that the distance from P1 to P4 be >= some minimum value. Same for P2 and P4.