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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The triple point
These three images show the 2-fold eversion near the time pairs of triple points are created, in a close up, a solid view, and a gapped view highlighting the double-locus.
Near the halfway stage of the 2-fold eversion, the double locus is quite elaborate, with a small tetrahedron growing out of what is the quadruple point at the halfway stage. A cutaway view of the halfway model is quite elaborate.