There are 432 enantiomorphous and 415 chiral fully supported stellations of the icosidodecahedron. Using Miller's rules gives 7071672 enantiomorphous stellations and an undetermined number of chiral stellations (Webb).
The first stellation is a dodecahedron-icosahedron compound.
The original icosidodecahedron oriented with a triangular face pointing upward, facial planes, and the intersections of those planes with the "top" facial plane are illustrated above.
The original icosidodecahedron oriented with a pentagonal face pointing upward, facial planes, and the intersections of those planes with the "top" facial plane are illustrated above.
The stellation diagrams showing the lines of intersections of nonparallel facial planes with the plane of a triangular and a pentagonal face are shown above (Wenninger 1989, pp. 74-75).
