Still Pictures of the Crosscap

Selecting a small picture will enlarge it.

The first two pictures show the surface from different viewpoints.

The segment of self-intersection (double points) is visible. The endpoints of the segment are pinch points, which are also visible.

The segment of self-intersection is tilted toward the front.

The next two pictures show the surface cut open.

Both pieces of the surface are shown tilted toward the front after the cut is made. The top piece is easily seen to be a Whitney Umbrella. The double points occur where two sheets of the surface intersect.

The top piece has been discarded and the bottom piece has been rotated. Again, the self-intersection may be seen more clearly.

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