Given a curve in the right half of the xy-plane, a twisted tube is generated by revolving this curve in space around the vertical y-axis, rotating it in the plane as it goes. The following immersion of the Klein bottle in 3-space is the result of revolving a figure-8 curve with a half twist (just as as the familiar Moebius strip is obtained by revolving a straight line segment with a half twist.
For details see the paper Twisted Tubes, The Mathematica Journal 3 (1993), 10-13, which generalizes the construction of the Klein bottle: We provide a Mathematica notebook that you can use to generate some twisted tubes for yourself.