Plan tread count, riser, and cantilever reach for a floating stair. Structural support must be engineered.
Floating (cantilever) stairs appear to project from a wall or a central spine with no visible support. The geometry is the same as a straight stair; the difference is structural. Each tread cantilevers and must be engineered for load.
Through an engineered system, commonly a hidden steel spine, wall-embedded steel, or a mono-stringer. Each tread cantilevers and must be sized for load by an engineer.
The geometry (riser, tread, headroom) follows the same code as any stair; the open risers must still reject a 4-inch sphere, and a guard or rail is required. The structure needs engineering.
Thick enough to carry the cantilever load, often 2 to 3 inches for hardwood over a steel core. An engineer sizes them.