Some Movies Showing the New Surface:

Level Sets (movie, 60K)

This movie shows the level sets for a model of the central real projective plane (minus two disks) of the tight surface.

The initial triangle is a minimum and the final quadrilateral is a maximum, and there is a single saddle in between, at frame number 29. The required triple-point is at frame 23.

These level sets closely resemble the ones originally drawn by Kuiper in [K2], where he describes a tight projective plane with two handles.

Slices (movie, 200K)

This movie shows the projective plane (minus two disks) building up through its different levels: each frame adds a little bit more to the surface, so that at the end, the entire surface is visible. Again, the critical level is at frame 29.

The outer faces (that make the "handle" formed by the convex envelope) have been removed in order to reveal the internal structure.

Fly-By (movie, 340K)

This is a short movie that flies around the central projective plane (minus two disks), so that you can see some of its interesting structure.