A round toroidal magnet does not radiate magnetic field in space because all the field lines are confined in the magnet. For non-circular toroidal magnet, it is thought that magnetic field leaks out only slightly. But rigorous theoretical and experimental studies that verify this hypothesis are rare. I have done a simple experiment to show how magnetic field leaks out from a non-circular toroidal magnet.
Magnetic field of a non-circular toroidal magnet http://pengkuanem.blogspot.com/2014/01/magnetic-field-of-non-circular-toroidal.html