THE REGULAR TETRAHEDRON EXTENSION OF LAGRANGES 3 BODIES

It is shown that four particles of any mass ratio on the vertices of a regular tetrahedron form an equilibrium configuration in expanding co smological coordinates. This configuration is unstable to all normal m odes of motion, although not violently so, and with a force law shallo wer than inverse first power it can become stable. Details of the inst ability are discussed using numerical calculations as well as group th eory. Applications to galaxy formation and the dynamics of small group s of galaxies are mentioned.