The answer to my previous question about the shape below is the Conway notation C969qD.
Per the linked viewer in that answer:
The specification consists of a space-delimited series of polyhedral recipes. Each recipe looks like:
[op][op] ... [op][base] no spaces, just a string of characters
I thought I might try to read through the notation to see if I could try to do this manually by manipulating shapes in Blender + Python, but I've gotten stuck trying to parse the procedure into steps that I can understand.
The operation is read right to left so the base is D which is dodecahedron, followed by some polyhedron-building operators C969q.
The final operator C969 is intriguing:
CN - proper Canonicalization, intensive, slow convergence, iteratively refines shape N times. Flattens faces. A typical N is 200 or 300.
Question: What exactly is it that needs to be done 969 times? Then how to apply q for quinto? All I see on the page is Thanks to "Lei Willems - for inventing quinto."
I see several dodecahedrons here for example, but no quinto.
Conway notation works right to left, as explained in the linked wikipedia page.
"quinto" -- as explained on the viewer page, but not the wikipedia page, replaces every face with a truncated pyramid, the faces of which are five sided. remove the C969 to see that.
The canonicalisation process isn't Conway, but attempts to convert the shape into as regular a shape as possible following an algorithm (basically make the vertices as equidistant as possible and convex). This implementation takes 969 iterations to converge the shape this implementaion makes for a qD. If you were to reduce the value to 968, you'd see a single blue face, which wasn't quite the same shape as the other 59 irregular polygons
k5oD also works - start with dodecahedron [D], create an edge orthogonal to every edge (o) (here this replaces every face with a pyramid, each face of which has four edges) then truncate all vertices with 5 edges (t5) - as it happens that construction, in that viewer, doesn't need any processing to make it ball-ish. The Conway wikipedia page talks about other methods of constructing a quinto-dodecahedron.
It so happens Conway operators have been implemented in Blender as a plug-in, but the viewer linked allows you to play with the different operators.