Möbius Strip as a Half-Twisted Square Torus

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

The square half-twisted torus can be changed into a Möbius strip if you shrink the square to a line segment, and vice versa. You can also change chirality to observe the isomers becoming mirror images of each other.

Contributed by: V. M. Chapela and M. J. Percino (March 2011)
Open content licensed under CC BY-NC-SA



There are four sliders: 1. Möbius sections 2. enantiomer (+1) or (-1) 3. Möbius and torus diameter 4. geometrical limit

The first slider makes the Möbius sections grow from 0 to 360 degrees. The Möbius strip is constructed from a large number of discrete cuboids that are rotated about a circle. This is similar to the torus, a surface of revolution generated by revolving a circle in three dimensions about an axis perpendicular to the circle.

The second slider, enantiomer or , changes the twist.

The third slider makes the Möbius strip and squared section diameter larger or smaller.

The fourth slider increases or decreases the rectangular pieces from a flat plate to a square cross section.

For more information, visit the following website:


Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.