Toroids are solids with genus, i.e. showing a number of holes in their surface. Here are a few Stewart Toroids (Toroidal solids with regular polygon faces) built with Geoshapes. Detailed information on these structures can be found at:
and in Bonnie Madison Stewart's book "Adventures among the Toroids",
Okemos, Mich. 1970 (2nd rev.ed. 1984)

Near Misses

Near Misses are polyhedra which are almost Johnson solids, i.e. their faces are nearly regular polygons, though not quite. More information on this subject can be found at: