The Final Circle:

Finally, the curve returns to a convex circle, as required for the top sets of a tight immersion [More]. Note that the polyhedral circle stars large, gets smaller toward the critical level, then grows larger again for this final step; this is in keeping with the fact that this projective plane forms the central M- region of the tight immersion [More] and should have "negative curvature" everywhere; that is, it should have the basic shape of a hyperboloid of one sheet: wide at the top and bottom and thin in the middle.

[Right] Movie showing the complete sequence of levels
[left] Level 7: No more self-intersection
[Left] Comparison to Kuiper's level sets
[Up] Other pictures

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9/29/94 -- The Geometry Center