Scherk towers and its deformations
From a distance the most symmetric Scherk tower of order k >= 2
looks like 2k vertical half planes (Scherk ends)
which are joined in such a way that they do not intersect.
So, these surfaces are embedded. In the most symmetrical case
there exist 2k straight lines on the surface.
In general the less symmetric Scherk tower
of order k is a one-parameter family.
A variation of the parameter effects a shaking of the ends.
Therefore in the less symmetric case the wings may intersect for order k >= 3.
How do I get the complete fundamental domain of translation
when using GRAPE?
The name of the input file is k_tower.am in case of the symmetric
Scherk tower and k_lsst.am in case of less symmetric saddle towers.
For a tower with 2k wings you need k+3 operations of reflection.
First reflect along the straight line. Then reflect on the
vertical boundary line. Now reflect along one horizontal line.
The result has to be reflected k times along a vertical boundary line.
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grape@iam.uni-bonn.de
