This is a set of Square Rhombic Torus builds.

The base shape is a regular Octahedron. Such a Torus can be built from Octahedrons and Tetrahedrons.

You might think that the cross-section would be square, but the traverses run at 45° angle compared to the square outline of the Octahedrons.

Parts list, all regular ½" Spheres and 58mm Geomag Rods:

Order-0: 6 Spheres, 12 Rods (base element: Square Bipyramid of equal edge length, i.e. an Octahedron)

Order-1: 17 Spheres, 48 Rods

Order-2: 32 Spheres, 96 Rods

Order-3: 48 Spheres, 144 Rods

I have no mathematical explanation for the exceptional sphere count of the Order-1 builds. I would guess that the center point of these is not a vertex, but some kind of singular inner point.

It's really hard to get a good perspective on these, because of obstructed rods. The Order-3 is missing two orange rods, which I realized afterwards.

Order-0 emphasizes the build as Square Bipyramid (Base edges: Black, Lateral edges: Grey). The others have dark rods for the main edges of the trapezoid faces, and bright rods for the edges of the triangulation of the trapezoids.