Table of Figures:

"

Movies:

1. Levels sets of the polyhedral surface (60K)
2. Building up the polyhedral surface (200K)
3. The polyhedral surface rotating (340K)

Interactive Pictures:

1. The complete polyhedral surface
2. The central projective plane

Geomview objects:

1. The complete tight surface
2. The central projective plane
3. The complete surface with transparent convex envelope

Views of the polyhedral object:

1. The complete surface from above
2. Front right corner, from above
3. Front right corner, from the side
4. Right-hand side
5. Back right corner
6. Front left corner, from above

1. Levels for the polyhedral object:
   1. The initial circle
   2. Pulling one side across the other
   3. Adding the triple point
   4. The triple point
   5. Completely across the loop, moving toward a saddle
   6. Just before the saddle
   7. The critical level
   8. Just after the saddle
   9. Pulling back toward the edge
   10. The final circle

2. Levels drawn by Kuiper:
   1. All levels
   2. The initial circle
   3. Pulling one side across the other
   4. Adding the triple point
   5. Just before the saddle
   6. The critical level
   7. Just after the saddle
   8. Pulling back toward the edge
   9. The final circle

(not yet ready)

1. The level sets for an immersed projective plane
2. Ruled surfaces to connect the levels
3. A tight two-handled torus
4. A tight Klein bottle with a handle

Miscellaneous:

1. Tight polyhedral torus, two-handled torus, and Klein bottle with a handle
2. How the triple point is formed within the level sets
3. Polyhedral analogues of cusps and folds
4. A Klein bottle
5. The M+ and M- regions for a Klein bottle
6. A Möbius band
7. An exotic polyhedral monkey saddle
8. Adding a polyhedral handle tightly
9. Some polyhedral surfaces that are not tight
10. The neighborhood of a non-bounding embedded curve on the projective plane
11. A tight torus and its decomposition into the M+ and M- regions
12. The triangulation of the projective plane that forms the tight model, together with its double curve
13. An immersed, but not embedded, topset