The Boy surface, cross-cap, and Roman surface are possible parametrizations of surfaces obtained by sewing this to the edge of a disk.
The Boy surface, cross-cap, and Roman surface are possible parametrizations of surfaces obtained by sewing this to the edge of a disk. Deforming these can create paradromic rings and they have Euler characteristic zero. Tori may be a cut one of these, and cutting a Klein bottle in half produces two of them. The B. F. Goodrich Company patented a conveyor belt in the form of this which lasts twice as long as conventional belts. These are also called twisted cylinders and are surfaces without a boundary. Identify this surface with only one boundary component and one side, which can be produced by half-twisting one end of a strip and attaching the two ends.
The Boy surface, cross-cap, and Roman surface are possible parametrizations of surfaces obtained by sewing this to the edge of a disk.
{Möbius strip}