The Möbius stip is the simplest geometric shape which has only one surface and only one edge. It can be created by taking a strip of paper, giving it a half twist along its long axis, and then joining the two narrow ends together.

The Möbius strip in 3 dimensions can be represented parameterically f(s,t) as follows

where s ranges from 0 to 2*pi and t ranges typically from -0.4 to 0.4

An example of such a strip is shown below.

Featured in "mama 27", November 2000, pp 91, Figure 17.

The band for different values of t are illustrated below.

t = -1 -> 1

t = -0.1 -> 0.1

t = -0.5 -> 0.5

Increasing the range of t even further yields interesting folded and increasingly convoluted forms.

x = 0.655866 cos(1.03002 + u) (2 + cos(v))
y = 0.754878 cos(1.40772 - u) (2 + 0.868837 cos(2.43773 + v))
z = 0.868837 cos(2.43773 + u) (2 + 0.495098 cos(0.377696 - v))
0 <= u <= 2 pi, 0 <= v <= 2 pi