I will tell you how I cut & fold each of what paper objects I try to make, then I will show you the designs in steps of what I did to create that, then you tell me if there’s better way to cut-fold to make that paper object.
The first that springs to my mind is the Dodecahedron, because I once made a pomander to that shape in sheet brass, as a Christmas present to a girlfriend. It has twelve facets, each a regular pentagon.
Your other post related to this asks about the Sphere. The development for that is a series of segments that if flattened, resemble ellipses with sharp major-axis tips. The sides must be arcs of the same radius as the sphere, but unless you can curve the segments across their widths to that radius as well, the "sphere" will be facetted. The minor axis of the segment must be of width equal to the circumference divided by the number of segments. Think of the segments of an orange.
