I'm not sure what the correct term is, but I'm thinking of objects that may contain polytope-like flat cells, but in addition may also contain curved elements like 3-manifolds. I was going to say toratopes, but then I wasn't sure if the category of shapes I have in mind is restricted to toratopes, since they could include more things like the convex subset of Bowers' polytwisters. Basically, I'm thinking of shapes that are approximable by polytopes, e.g., the duocylinder is approximated by m,n-duoprisms as m and n approach infinity; the bicircular tegum is approximated by m,n-tegums as m, n approach infinity, etc..

Anyway, terminology isn't my primary concern here. What I wanted to ask was, is it possible for such an object to be both convex and contain a 2-manifold surface element that's non-orientable, like a Mobius strip? I.e., in the approximating polytopes, you'd have a circuit of polygons that approximate a Mobius strip, but everything else would still fit together "traditionally" and form a convex polytope (as an approximation to the limiting shape). Can such an object exist?