Two problems we can ask:
1. Systematic tiling rules for P- and D-type Schwartizes. This problem probably has been solved by Chuang and Fan already. But I haven't seen their works yet.
2. Possibility of constructing other triply periodic minimal surfaces based on trivalent sp2 network. A quite complete list of triply periodic minimal surfaces can be found here:
triply periodic minimal surfaces
One can find more pages on minimal surfaces through google search.
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