As another top-level comment mentioned, depending on the sheer strength, it could be used in composite structures.
Take a 2'x2' 1" thick piece of foam. Laminate some fiberglass onto both sides of it. This is basically how modern boat hulls are constructed. Extremely light, rigid, insulated and durable.
WAG, but if it would allow you to replace 1 ton of foam on a 40' yacht, that's one ton of extra cargo/amenities you could carry instead and maintain the same water line. Or alternatively you could produce a faster boat with less wetted area.
I'm sure a real engineer has a better idea of practical applications. But I like cruising yachts so. :-)
1 ton of foam? Foam used in boating is usually in the 2-4lb range, which means 2-4lb per cubic foot. There's not much chance a 40' yacht has 1000 cubic ft of foam in it - far more likely it's got 20-30 cu ft, which is under 100lbs of foam. Not enough to move the needle a bit.
Plus, foam provides displacement in case of breaches as a matter of it's nature. This lattice wouldn't provide any displacement, so a small breach would mean you're 2" thick composite hull would fill with water, which would be bad.
Just by looking at it, I doubt there is enough shear strength to make it a useful sandwich panel web. Then again, I've been wrong before. But metallic/composite honeycomb is pretty well optimized stuff as it is.
Take a 2'x2' 1" thick piece of foam. Laminate some fiberglass onto both sides of it. This is basically how modern boat hulls are constructed. Extremely light, rigid, insulated and durable.
WAG, but if it would allow you to replace 1 ton of foam on a 40' yacht, that's one ton of extra cargo/amenities you could carry instead and maintain the same water line. Or alternatively you could produce a faster boat with less wetted area.
I'm sure a real engineer has a better idea of practical applications. But I like cruising yachts so. :-)