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This is the article that covers (briefly) the investigations of the mechanical
properties of gyroids, particularly as a structure that might be possible with
graphene. The other links are the direct sources. It seems like it might be an
ideal structure to use as fill in 3d printed parts. I've not seen it as an
option on any of the slicers so far though.
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It looks like somebody else thought it would be good too - it was added to
Slic3r in February 2018 after a feature request in 2017. There was some
discussion of how to test it to find out if it was structurally better than the
existing 3Dhexagon fill. If you want to test it you'll need one of the 1.3.0-
dev automated builds as 1.2.9 is _much_ too old.