The following images are stills taken from The Optiverse, a video by John Sullivan, George Francis, and Stuart Levy, about the minimax sphere eversion.
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Composite of the 2-fold minimax eversion
Clockwise from upper left, we see stages in the eversion. Images on the right show the creation of triple points (top pair) and passage through the quadruple point at the halfway stage (bottom pair). The large middle image shows the halfway model from the other end, where there is a point of double tangency.
Composite of the 3-fold minimax eversion
Clockwise from upper left, we see stages in the eversion. We can see how three fingers grow into each other. The two views at the bottom with gaps between the triangles show the halfway model (Boy's surface) and the way it breaks apart into its double cover. The large middle image is close to the halfway stage.