The Initial Self-Intersection:

Here, the left-hand side has passed through the right-hand side, causing self-intersection within the surface. Note that in the polyhedral model (right), the lower loop is already beginning to intersect the upper one, anticipating the action to come in the next step.

[Right] Level 4: Adding the triple point
[Left] Level 2: Pulling one side across
[Left] Comparison to Kuiper's level sets
[Up] Other pictures

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8/10/94 -- The Geometry Center