  We study the rhomboidal symmetric-mass 4-body problem in both a
two-degree-of-freedom and a four-degree-of-freedom setting. Under suitable
changes of variables in both settings, isolated binary collisions at the origin
are regularizable. Linear stability analysis is performed in both settings. For
the two-degree-of-freedom setting, linear stability is established for a wide
interval of mass ratios. A Poincar\'{e} section analysis is also performed,
showing stability. In the four-degree-of-freedom setting, linear stability
fails except for a very small interval of mass ratios.
