The Klein Bottle

A closed nonorientable surface that has no inside or outside.
The Klein Bottle can be constructed by gluing both pairs of opposite edges of a rectangle together giving one pair a half-twist.


  • Move the "How to build" slider to see an animation of its construction.
  • Click on some Elements while holding down the 'n' button to mark them. Now you can keep track the element's movement when moving the "shift" slider.
  • Reset all values and then set the "uMax" slider to 1.57 ( ~ pi/2). Now slowly increase the value of "vMax". What do you get?
  • Move the "Moebius Strip" slider to cut open the Klein Bottle to a Moebius strip.
    A Moebius strip is a one-sided, nonorientable surface that is obtained by cutting a closed band into a single strip, twisting one of the strip's ends by 180 degrees, and then reattaching the two ends.

© 1996-2012 Last modified: 29.10.2012 --- Konrad Polthier --- Freie Universität Berlin, Germany