Besides the Lübeck-Batista surface, there is at least one other doubly periodic minimal surface of genus 3 that could be dubbed a doubly periodic Callahan-Hoffman-Meeks surface. To my knowledge, this surface doesn’t appear in the literature and is currently only numerically established.

Here, the surface maintains the reflectional symmetries from the Costa saddles but loses all straight lines. The Callahan-Hoffman-Meeks surfaces appear to be rotated by 45º compared to the  Lübeck-Batista surface. It would be very interesting to know whether these surfaces can be minimally deformed into each other through a continuous rotation of the CHM surfaces.

At the other limit, the surfaces apparently converge to 8-ended Scherk surfaces, stitched together using catenoidal necks.


Mathematica Notebook

PoVRay Sources

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s