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.

Its convex hull is an equilateral truncated chamfered dodecahedron, with 12 decagons, 30 equilateral dodecagons, and 80 triangles (divided into two sets of 20 and 60). It can be obtained as the Minkowski sum of a rectified chamfered dodecahedron and a truncated icosahedron.

The toroid was first described by Robert Webb, creator of the proprietary polytope software Stella.

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. The convex hull would remain equilateral, but would no longer be a near-miss Johnson solid. Instead, it would be the Minkowski sum of a rectified chamfered dodecahedron and a regular dodecahedron. It would maintain the 12 decagons and 80 triangles, while the dodecagons would "contract" into rectangular-symmetric octagons (which would appear somewhat squashed). If the perpendicular edges of these octagons are further "contracted" into points, it yields a rhombus with one diagonal double the length of the other.