Dini's Surface
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Introduction:

The twisted pseudosphere is called Dini's surface. Like the pseudosphere, it has constant negative Gaussian curvature.

Definition:

Properties:

Tangent Planes:

At u = u0, v = v0, the tangent plane to the surface is parameterized by:

Infinitesimal Area:

The infinitesimal area of a patch on the surface is given by

Gaussian Curvature:
Gaussian curvature of the surface.
Surface colored by Gaussian curvature.

Mean Curvature:
Mean curvature of the surface.
Surface colored by Mean curvature.