Brendan Quine - Thothx Space Elevator (time-stamp 1) | time-stamp 2
They built a 3 story test version. They describe wrinkling as a problem. I like that it is a tube, not a giant cylinder, and is made out of smaller cells, which makes the hoop stress much less of a problem, and makes it easier to manufacture.
Assuming AWE does not need to send elevators up and down, you could make a smaller, lattice tower version. I would combine the concept with Tensairity, and a tensairity torus idea which I think basically solves the wrinkling problem and makes the beams/cells 10-100 times more resistant to buckling.