I have no 3D intuition. I began to render math models using a ray-tracing software (Povray). But I needed to draw several images to get an idea of the 3D aspect of those models. Then I began to learn Blender, in order to be able to turn around my models. Next step was to ask a 3D printing company to create real-world models. I can know handle my creations, and look at them from any angles in a second. Here is a selection of those tries.
Cardioidal variation I
A shape derived from the Pedoe method for generating a cardioid. This object is used by the rock group Marillion for the cover of their 17th album.
Following the edges of the icosidodecahedron I
Putting squares on the edges of the icosidodecahedron.