The usual version of a Möbius strip has as its single boundary curve an unknotted loop. An unknotted loop can be deformed into a circle, with the strip deformed along with it. In this version, the boundary of the strip is the circle in the middle, and the surface "goes through infinity", meaning that the grid pattern should extend outwards all the way. To save on costs, I've removed the grid lines that would require an infinite amount of plastic to print.
This was designed with the assistance of Saul Schleimer.