A walnut inlay in Baltic birch.
I see that others have posted on these tensegrity structures. The prototypes shown here use a 4-hole symmetry for the outside tensioning line made from a single length of 10 LB test woven fishing line. A splicing knot completes the tensioned outside line loop.
This symmetry and line stringing allows orthogonal X,Y leveling of the top and bottom after tensioning. The line is then epoxied into hidden horizontal engraved channels to prevent sliding or tipping. Zig-zag stringing could be used for increased twist stability at the expense of visual effect.
Brass pins and a portion of one of four hidden engraved channels are shown below.