The classic bascetta star (second from the left in the picture of five models) consists of twenty spikes. Mathematically speaking you could see it as spike erected on each side of an icosahedron. The other four models are made using the same technique but applied to a different platonic solid each. By the duality of the icosahedron with the dodecahedron the spikes of a model based on one of them can be interpreted as the corner points of a model of the other one. A similar thing can be observed with the cube and the octahedron, as well as for the tetrahedron with itself. The other two models show the classic bascetta star, but bigger. Instead of one triangular spike per side of the icosahedron, four and nine were used respectively.
Nadja Vohradsky is an undergraduate student at Lincoln College.