Could triangular DNA exist?
This is sort of a follow up on my question Could a "multicellular" virus exist? in which part of the consensus was that viruses simply can't hold enough DNA. In theory, could DNA form in a structure such that instead of looking like a line on the end it looks like a triangle? This would then have three times the storage, and my previous idea is slightly more plausible. Could this exist with the benefit of more storage/complexity? What disadvantages would it have? Some handwaving is allowed.
Could triangular DNA exist and what would the tradeoffs of it be?
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Sort of.
A structure similar to the one you describe can in fact form. Triple-stranded DNA can be stable under certain conditions. Two bases bond via slightly different structures, and a third base bonds via something called a Hoogsteen hydrogen bond. In this manner, three different strands of DNA can be brought together, rather than just two. The formation process is slower than for a normal double helix, but it remains extremely stable. Looking down the helix, it would indeed appear triangular in shape.
I find it a bit unlikely that this would lead to a higher information density. Normally, the only allowed combinations of base pairs are adenine-thymine and cytosine-guanine. Here, a third strand means you can have more than two triplets. However, not all triplets are equally stable (in fact, CG*C+ and T*AT are very much the most favored), so it's not like you really have eight viable possibilities instead of two. I'd be exceedingly surprised if this really was a substantial improvement over the double helix, even just from an information storage perspective.
It's also not clear that triple-stranded DNA would evolve as the dominant structure. It occurs naturally in organisms, but only in small amounts. Why? Well, we don't know for sure, but one downside is that more complicated, and therefore more prone to mutations - it's not like transcription is easy. This is going to affect any more complicated structure of DNA beyond the typical double helix. I would assume it's unlikely to be selected for evolutionarily as the main structure for storing genetic code.
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