Riemann's surface

From a distance this surface looks like parallel planes joined with necks which lie on a straight line. Modulo orientation preserving translation there are only two planar symmetry lines and two parallel straight lines. They cut the surface into four simply connected pieces. Riemann's surface has no self-intersections (it is embedded).



How do I get the complete fundamental domain of translation when using GRAPE?

The input file name of these surfaces is riemann.am.

First of all you should load the grid-status-file to see the computed piece of the surface. This piece is bounded by one planar geodesic line, one straight line and an other line which contains a point where 180-degree rotation around the normal of the surface is a symmetry. Now you have to find the point with rotational symmetry. After this normal-rotation reflect the surface along the planar geodesic line, and rotate around the straight line. If you read in the patch-status-file, you will see the fundamental domain of translation of this surface. You can continue it by rotation around the straight lines.


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