Webb toroid

The Webb toroid is a toroidal polyhedron. It can be obtained by outer-blending twelve tunnelled pentagonal rotundae, sixty pentagonal antiprisms, sixty pentagonal prisms, and twenty tridiminished icosahedra together.

Related polyhedra
A similar figure to the Webb toroid can be made with ordinary pentagonal rotundae instead of tunnelled ones. It would have genus 29, and naturally the convex hull would not change.

Its pentagonal prisms can also be removed (while bringing the other components together), and the toroid would maintain its quasi-convexity and genus. However, the convex hull would no longer be a near-miss Johnson solid. Rather than the near-miss dodecagons of the original, the new convex hull would have thirty rectangular-symmetric octagons, similar to those of the truncated rhombicosidodecahedron but not the same. If the perpendicular edges of these octagons are "contracted" into points, it yields a rhombus with one diagonal double the length of the other.