A toroidal internal magnetic field does not "leak" outside of the torus and contains all the energy inside. This is a good property to describe mass. I believe that this internal magnetic field is what tenses space-time around it, which is another good property to describe mass. A third requirement/property is that this toroidal internal magnetic field should use all the dimensions of the space it is intersecting. For flatland, the internal toroidal magnetic field is a circle and fulfill this requirement. For space-land, this magnetic field has to have three dimensions. This is new. A way to imagine this is that the hypertorus produce an spherical internal magnetic field.
The field outside this hyperdimensional toroidal internal magnetic field is the gravitational field. This is better illustrated like this,
The difference between 2D and 3D space bending. One circle (2D object) is enough to bend 2D space in time. To bend 3D space you need a 3D object.