Here you can download 3D models of the following three different mathematical surfaces: helicoid, hyperbolic helicoid, and a surface obtained by transformation of the helicoid into catenoid.

All of them belong to a mathematical surface family called ‘minimal surfaces’. We hope some of you will find them to be useful. By the way, you can generate such surfaces in the free K3D Surf software (now MathMod). Unlike the mentioned software, we also offer you a NURBS 3D model of each of the mentioned helicoid surfaces.

 

Helicoidal 3D surfaces
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 software native file format)

Catenoid helicoid mesh - Quads only; Vertices: 945; Edges: 1824; Faces: 880

Helicoid mesh - Quads only; Vertices: 473; Edges: 892; Faces: 420

Hyper helicoid mesh - Quads only; Vertices: 1785; Edges: 3464; Faces: 1680

Mesh topology supports multiple subdivisions; 3D model without texture and materials;  Mesh have naked edges. 

 

The helicoid geometric surface was explained by Euler in 1774 and owes its name to its resemblance to the helix. It should be noted that the helicoid is also a ruled surface, i.e., a surface formed by the movement of a line. It can be said that for every point on the surface there is a line passing through it. In short, if you are interested in mathematics or want to create a math-art 3D model using one of these helicoid surfaces, feel free to download the 3D models offered here. Believe us, we will be very happy if at least some of you do it, and if you manage to practically use any of our 3D models, there will be no end to our happiness!

 

Download 3D model (BREP and NURBS)
Download 3D model (polygonal mesh)