Toruses

Replace 2 and 4 by thickened toruses 2′ and 4′ enclosing 3′ and replace 1 and 5 by the remaining regions.

Since we're discussing cosmic geometry, I will mention that the rings of angels are what mathematicians call toruses or anchor rings—i.e., doughnut-like shapes.

Germain Kreweras ... enumerated spanning trees on grids, cylinders, and toruses, as well as oriented spanning trees on directed toruses such as Oₘ × Oₙ.