Let’s say that an n-band is obtained by gluing together the left and right edges of a rectangle with n half-twists, where a half-twist is a half revolution ( radians). For example, the cylinder is a 0-band and the Möbius band is a 1-band. The following program creates a range of n-bands.

More bands

The program suggests that n-bands are two-sided and orientable for even values of n, and one-sided and nonorientable for odd values of n.

An n-band is generated by sweeping a line segment along a circle it is perpendicular to and, while sweeping, rotating the segment around its center to produce n half-twists, the total amount of rotation equal to radians. For example, to build a Möbius band (1-band), the line segment rotates a half revolution ( radians) over a complete sweep along the circle.

Möbius bands, and twisted bands (helixes) generally, have chirality, meaning they come in both right-handed and left-handed forms. This depends on the sense — clockwise or counter-clockwise — of the twisting rotation. In the program, positive values of half twists produce right-handed bands, and negative values left-handed bands.