Morin surface

The following is a summary of the eversion: 1. sphere: green outside, red inside... 2. transforms into... 3.

The Morin surface has a quadruple point through which passes its axis of symmetry.

The diagram shows section East bounded by three loops: ABCDA, AEFGA, and AHIJA.

The third loop, AHIJA, is a line of double points where section East intersects with itself.

Morin surface can be elegantly described by a set of equations[1] in either open version (with poles sent to infinity) or closed.

Morin surface seen from the top
Morin surface seen from the side
paper sphere eversion and Morin surface
paper Morin surface (sphere eversion halfway) with hexagonal symmetry