Is it going to be strong enough? I remember reading some article about a year ago that mentioned diamond and some kind of carbon fiber, but concluded that even with the maximum strength that molecular bonds can develop no material would be quite strong enough to support its own weight. I don't know for sure just asking if anyone has seen any recent research on the topic.
If I recall, the hextube idea was Robert Forward’s work around. There was a specific braiding pattern he described where if one fiber broke, the force would be routed around the break and back to the original fiber. It certainly wouldn’t be a single strand but more of many cables made up of many strands formed into a mostly open space tube or ladder.
It was part of his work around for his fiction. In Saturn Rukh he used nanofiber tethers fired into asteroids from spaceships to make hard turns putting considerably more force on the tether than it could bear. He got around the problem with a braking system that is essentially like the drag on a fishing reel.
Forward was widely known as a science fiction writer but he was the real deal physicist with the credentials to back it up. https://en.wikipedia.org/wiki/Robert_L._Forward
Obviously the space elevator is a different application but the force is divided between the earth anchor point and space anchor point with an adjustable weight system that moved up and down from the 26,000 mile point.