Looks like such a planet would have some odd-looking periodic orbits: http://arxiv.org/abs/1108.4635 http://arxiv.org/abs/1108.4635 One family of orbits is par

Looks like such a planet would have some odd-looking periodic orbits: http://arxiv.org/abs/1108.4635 http://arxiv.org/abs/1108.4635 One family of orbits is parallel to a face of the cube, if I understand the paper even a little.