# Thurston Sphere Eversion

This video shows a sphere eversion using Thurston's corrugation method, as described in the video Outside In by the Geometry Center (Bill Thurston, Silvio Levy, Delle Maxwell, Tamara Munzner, Nathaniel Thurston, David Ben-Zvi, Matt Headrick, et al.), 1994, and the accompanying booklet Silvio Levy: Making Waves — A Guide to the Ideas Behind Outside In, A K Peters, Wellesley, MA, 1995.

An eversion turns the sphere inside-out in a smooth manner. Creases, pinch points, holes, etc. may not occur. However, the sphere may intersect itself during the eversion. In mathematical terms, the eversion is a regular homotopy between the sphere and the sphere point reflected at its center. To indicate the two sides of the sphere, its outside is colored gold and its inside purple.

The video has four parts. In the first part, an eversion of the complete sphere is shown. Conceptually, the sphere consists of eight spherical lunes that all deform in the same manner. First, the sphere is corrugated. This is necessary to add enough pliability for the following steps. Second, the northern and southern parts of the sphere are pushed through each other. This causes loops in the central part of the sphere. Third, the northern and southern part of the sphere are rotated by 180° in opposite directions. At the same time, the central part is twisted to remove the loops. Fourth, the central parts of the sphere are pushed through the vertical axis of the sphere, which moves the outside parts of the center…

- Kind: Short
- Year: 2022
- Runtime: 1 min
- By: Carsten Steger
- Archive: [Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Thurston_Sphere_Eversion.webm)
- Licence or status: [CC BY-SA 4.0](https://creativecommons.org/licenses/by-sa/4.0) (as the archive states it)
- Credit: Carsten Steger
- Who can watch: Teens profiles and older (the archive gives no rating; placed by Invisible Network from its collection and subjects)

[Watch now](https://invisiblenetwork.ai/watch/archive/commons/114135293?play=1)