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We construct a highly-symmetric periodic orbit of six bodies in threedimensions. In this orbit, binary collisions occur at the origin in a regularperiodic fashion, rotating between pairs of bodies located on the coordinateaxes. Regularization of the collisions in the orbit is achieved by an extensionof the Levi-Civita method. Initial conditions for the orbit are foundnumerically. In contrast to an earlier periodic collision-based orbit in threedimensions, this orbit is shown to be unstable.

The Octahedral Collision-Based Periodic Orbit in the Three-Dimensional Six-Body Problem