An Icosahedron has 17 fully supported stellations: 15 reflexible and 2 pairs of chiral twins. The vZome model shows how each of these can be build:

Building Instructions

A magnetic set of building blocks, able to construct all stellations, requires eleven different types of cells: 9 reflexible and 1 pair of chiral twins. The colouring scheme has been chosen in such a way that the compound of five tetrahedra (probably the best known stellation), has a dedicated colour for each component. By this, even the reflexible stellations look chiral after colouring. All fully supported stellations have actually been built, as shown in the following pictures:

Icosahedron
Triakis Icosahedron
Compound of Five Octahedra
D Stellation
De1 Stellation
De2 Stellation
E Stellation
Compound of Five Tetrahedra
Compound of Ten Tetrahedra
Great Triambic Icosahedron
Ef2 Stellation
Ef1f2 Stellation
F Stellation
Excavated Dodecahedron
Fg1 Stellation
Fg2 Stellation
Great Icosahedron
Echidnahedron