Doubly Periodic Surfaces |
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The most basic doubly periodic surface was discovered by Scherk. It comes in a family with varying angle between the top and bottom planar ends. This family gives all the embedded doubly periodic surfaces of genus 0. |  56 K Quicktime Movie |
| For higher genus, the zoo grows. To the right you can see a Scherk surface with a handle. Below are two different doubly periodic surfaces with parallel top and bottom ends. They belong to a family which shears the handles along the ends. The right hand one can be interpreted as a fence of singly periodic Scherk surfaces whith planar ends glued together. |
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| Similarly, the right hand surface can be seen as a fence of copies of the singly periodic Riemann minimal surface: |  |
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