A Geometrical Sculpture Inspires a Geometrical Construction

While doing my Holiday shopping at the Derby Street Mall. I came across the polyhedral sculpture shown in Figure 1a. Examining it carefully I saw that it had 12 Pentagonal pyramids sticking out from a dodecahedral core. I suspected it was a transformed Kepler‑Poinsot Regular non‑Convex Polyhedra known as a Small Stellated Dodecahedron shown in Figure 1b. This fascinated me so this Geometer’s Corner column will be about how to use GeoGebra to build both a Small Stellated Dodecahedron and the Derby Street Structure. Much of what I am going to describe I got from the article The Four Regular Non‑Convex Polyhedra which can be found at:

https://cage.ugent.be/~hs/polyhedra/keplerpoinsot.html

The Small Stellated Dodecahedron is regular but its faces are not regular polygons but rather are Pentagrams.