  We construct a highly-symmetric periodic orbit of six bodies in three
dimensions. In this orbit, binary collisions occur at the origin in a regular
periodic fashion, rotating between pairs of bodies located on the coordinate
axes. Regularization of the collisions in the orbit is achieved by an extension
of the Levi-Civita method. Initial conditions for the orbit are found
numerically. In contrast to an earlier periodic collision-based orbit in three
dimensions, this orbit is shown to be unstable.
