In Newton's equations of motion, the mechanics of a rigid body is completely specified by the 0 th , 1 st and 2 nd moments of its mass distribution, namely the total mass (M ), the center of mass (CoM) vector (R), and the inertia tensor (X). Therefore, one is free to alter the positions of a set of rigidly connected, massive, non-interacting particles as long as M , R, and X are kept constant, without altering the equations of motion. Sets of points that possess the same M , R, and X are called equimomental systems. Naturally, to preserve the dynamics of the system, the mass-less interacting sites must be subsequently reconstructed around the new "scaffold" of massive non-interacting particles. This well-known concept is the basis of virtual sites in MD. While finding equimomental systems is trivial for rigid linear molecules, it becomes increasingly complicated for planar and non-planar molecules due to couplings between M , R, and X. Recently, Laus and Selig presented a general procedure to generate equimomental systems from a regular tetrahedron. Here, we only present a brief outline of the theory.