A One-Sided Question

The puzzling Rich Laver asked me this one, at Saturday night's CFOOTMAD dance, in Boulder.

Imagine a three-dimensional Moebius strip -- a strip that has not just width, but thickness. We're talking a strip that's a foot wide, 50 feet long, and also an inch high. Next slice it through the waist, all the way around the strip, and pull apart the half-inch-thick, top and bottom halves.

What do you get?