Polyhedra playground

Start from one of the five Platonic solids. Then truncate its corners, take its dual, stellate it into a star, or facet new faces between its corners - and chain them freely: a stellation is not a dead end, so rectifying the small stellated dodecahedron gives the dodecadodecahedron. The recipe reads right to left: tI is truncate applied to the icosahedron, which is the soccer ball.