Here you can download five math art 3D models, whose common feature is that they all  originated from the initial 3D model of the truncated icosahedron.

With the first two models, we squeezed out certain faces and then made sphere-like bodies from these extrusions. With the fourth and fifth 3D models, we made a wireframe 3D model from the initial 3D model of the truncated icosahedron. The model in the middle is similar to the last two, but we also deleted certain faces so that some kind of dish was obtained. The modeling of all five models is very easy in Blender 3D software in case you have a 3D model of the truncated icosahedron. While on the subject, the truncated icosahedron is a polyhedron consisting of 12 regular pentagonal faces and 20 regular hexagonal faces, and it is known worldwide as the soccer ball (football). On soccer balls, the hexagons are usually painted white and the pentagons are painted black.

 

Math art 3D models based on truncated icosahedron
3D CAD software used for modeling

 

- Topmod and K3DSurf for modeling

- Rhino 3D and T-splines plug-in for conversion to NURBS 3D surfaces

Available NURBS and BREP file formats

Surface 3D model - .igs (Initial Graphics Exchange Specification)

Available polygonal mesh file formats

.obj and .blend

Mesh - Mesh topology supports multiple subdivisions; 3D model without texture and materials; Mesh does not have any degenerate faces, non manifold edges, naked edges, faces with directions different from the mesh as a whole, self intersecting faces...

 

You can print these 3D models on a 3D printer, make futuristic and abstract desktop wallpapers from them, or use them as initial models for designing more complex math art models.