Here you can download a 3D model of a sphere with a stereographic projection of Cartesian coordinate grid. We called it Stereographic sphere 3D model (Stereosphere 3D model).

In geometry, the term ‘stereographic projection’ refers to the projection of a sphere from some point onto a plane.  Stereographic projection preserves the angles at which grid lines cross each other. On the other hand, stereographic projection does not preserve area, the areas of the grid squares shrink as they approach the pole. You can see these two claims in the picture of our 3D model.

 

Stereographic sphere 3d surface
3D CAD software used for modeling

K3DSurf (MathMod software)

Available NURBS and BREP file formats

Surface 3D models: .igs (Standardized 3D graphic exchange file format) and .3dm (Rhinoceros software native file format)

Available polygonal mesh file formats

.obj and .blend (Blender 3D graphics software native file format)

Mesh - Quads Only; Vertices: 2025; Edges: 3960; Faces: 1936; 3D model without texture and materials; Mesh has naked edges.

 

If you like to model math art 3D models, we are sure that you can use this one here. By deleting or extruding certain faces or edges, adding thickness, etc. you can obtain extremely interesting 3D shapes that can even become real-world objects if you have a 3D printer. If you are imaginative, with this sphere an interesting math art 3D model can be obtained that, after printing, can be transformed into a futuristic lampshade, fruit basket, etc.

We have given you an initial idea and an initial 3D model, and the most interesting task will depend on you - to design your own math art 3D model and make a useful object from it.