The extended version of Robert Webb’s Genus-41 Toroid is large enough to encompass Bonnie Stewart’s Holey Monster and a spherical layer of Triangular Cupola’s (J3’s). If one could connect each triangular face of the inner boundary of the Genus-41 to a hexagonal face of the outer boundary of the Holey Monster through a J3, than the Genus could be extended to a whopping 106.
The second scene of the vZome model shows a Holey Monster (green) and a antipodal set of a J3’s (purple) which are supposed to connect to the Genus-41 toroid. Of the latter, only two J63 fragments (red) are shown.
Unfortunately, the J3’s height is about 1/8 to short to make contact with both toroids. The only way to salvage the problem is shown in the third scene: shift the Holey Monster a bit so that at least one of the twenty tunnels can be made. This result in a Genus-87 toroid:
genus = 1 + (#edges-#vertices-#faces)/2 → 1+(3708-1238-2298)/2 = 87
A cunning idea ! Not worthwhile though to build physically.