Well this is a question that could have been answered a decade ago
I was looking into the toratopes again, and came to the Toraspherinder page. Now I know I originally wrote this, but it says "It can also be formed by taking an uncapped cubinder and connecting its ends in a loop."
Well... now that I think about this... how can you connect the ends of a cubinder? Unlike a cylinder or a spherinder, a cubinder doesn't really have two "ends"! Should I be connecting diagonally opposite circles, or orthogonally opposite cylinders? Both? Is this entire concept impossible?
Working very loosely with an extension of the abstract polytope concept to curved shapes, I've come up with an analogy that says a toracubinder should have four tubular faces in addition to its sole tubular cell, but this is probably completely wrong...