These stellations are made in the same manner as a foldup polyhedron - but the faces are chosen deliberately (and involve some complicated combinations of polygons) so that a stellated polyhedron is the result, rather than a simple polyhedron
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1. Constructed by extending edges to meet. file
2. Constructed as a fold-up. Rather more interesting! file
file 1 This is a foldup icosahedron - important to work out how this was made before trying a stellation
file 2 A foldup of one of the simplest icosahedron stellations
file 3 A stellation diagram. All faces are formed of a subset of the polygons in this diagram (google on Stellations to find out more about this)
file 4 A Kepler-Poinsot polyhedron: the one stellation of the icosahedron which is a regular polyhedron in its own right
file 5 This one folds into other interesting collections of polyhedra
file 6 file 7 file 8 file 9 Further examples
file 10 file 11 These two have rotational, but not reflective, symmetry.