More Framework

RT with 30 tent poles, red stabilizers

The most spherical of the identically faced polyhedrons is the 120 Triangles, which has other names as well, and of course a dual, the truncated icosidodecahedron. We see this shape being considered in the search for a volume five, in tetravolumes, for the core design of the Synergetics matryoshka, the nested polys (tet, cube, oct, RD, RT etc.). RT one the contest (rhombic triacontahedron).

The source code below shows the framework in action: create an RT of the canonical size (every shape has a default starting size); compute the 30 diamond face midpoints and extend them further out from the shape center by 5%. Draw red edges from these "tent poles" to each vertex of the corresponding face.

The transparent version is a mess of edges, so as a final step I bring the starting RT in, with faces filled (f=True). That brings the red edges of the 120 Triangles into sharp relief, and helps us judge whether convexity is maintained. If the tent poles poke out too far, this thing becomes a stellate, a planet with mountains and valleys. We want only mountains (convex creases).

The signature Catalan, dual of an Archimedean, has a specific tent pole height, whereas I'm looking at wiggle room. I discuss this difference in more detail on Synergeo.

 

Python source