This is a surface 3D model of the Mobius strip  (also spelled Moebius, Möbius strip, also band, or loop).

Mobius strip is a surface with only one side and only one boundary i.e. a surface formed from a rectangular strip by rotating one side of it by 180 degrees and pasting it to the opposite side. As you can see in the picture, this is a low-poly 3D surface  (supports multiple subdivisions), and based on it, we have created several math-art models that you can see here: Two math art 3D models based on Mobius strip.

 

Mobius strip 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: 285; Edges: 508; Faces: 224; 3D model without texture and materials; Mesh has faces with directions different from the mesh as a whole; Mesh has naked edges.

 

Otherwise, the Mobius strip is very easy to model in both NURBS and polygonal mesh 3D software, and there are numerous internet tutorials on how to do it. If you don’t feel like  modeling, just download our 3D model and use it to create some more sophisticated math-art 3D models, an interesting sculpture perhaps, and print it on a 3D printer; you may equally design an interesting necklace pendant, ideas are simply inexhaustible. If you are a beginner, why don’t you try creating your own 3D model of the Mobius strip in the software you are using!?