Draw an infinite subgraph of the 3d integer lattice in which each vertex has four co-planar neighbors, in a perpendicular plane to each of its neighbors. This completely determines the subgraph, which is 4-regular and highly symmetric. It is the graph of adjacencies of the cubes in this structure: https://en.wikipedia.org/wiki/Tetrastix . Does this graph have a name and history?
@11011110 The answer to your question appears to be "no", and a few people have done some investigation.
Are you still interested?
Do you have an email address for contact, or would you rather continue here?
@ColinTheMathmo Sure, especially if you have published references that might help beef up the Wikipedia tetrastix article. My email is linked from my home page linked from my profile here, but less indirectly it's firstname.lastname@example.org
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