A synergeoist on Synergeo wondered by what factor we would scale the icosahedron of edges one, to give it a volume of 20, i.e. what would the new edges have to be?
We think of the Jitterbug Transformation and how s_factor = jb_cubocta / jb_icosa (snake case) i.e. jb_icosa times s_factor takes its volume from 18.51... (tetravolumes) to 20 (ditto).
In other words, the factor in question is a 3rd root of the s_factor, since the latter scales volume, meaning its 3rd root is our linear multiplier.
The s_factor appears again when we morph the icosahedron into a cuboctahedron by a different route. Start with the icosa with faces flush to an octahedron's. Rotate the tilted triangles to a minimum volume 2.5 cuboctahedral conformation. Two applications of 1/s_factor does the trick.
