the concave regular

stellated dodecahedra

the following is a grasshopper definition that illustrates how the pentagonal dodecahedron generates:

  1. a regular icosahedron, by rotation of its faces;
  2. its first stellation, the small stellated dodecahedron;
  3. its second stellation, the great dodecahedron, whose convex hull is the icosahedron shown in the first step,
  4. the third and final stellation, the great stellated dodecahedron;
  5. in a subsequent step, it is shown how the small stellated dodecahedron transforms into the great stellated dodecahedron.