[whvosvec] Icosahedron stellations

The stellation diagram of one face of an icosahedron has 67 regions of finite area: 18 which are in 6 sets of 3, 48 which are in 8 sets of 6 with bilateral symmetry, and 1 central triangle.  If we ignore the bilateral symmetry, there are 22 sets of 3 plus the central triangle.  Therefore, there are 2^23-1 = 8388607 stellations of the icosahedron which satisfy Miller's conditions (i), (ii), and (iii).  Minus one because we omit the empty set.

This is considerably more than the 59 icosahedra of Coxeter, et al.  These polyhedra are more like collections of faces floating in space, not making any attempt to enclose a volume or have faces meet at edges.

In addition to the 67 regions of finite area, there are 18 half infinite strips and 18 infinite wedges, or 12 sets of 3 infinite faces.  This pushes the count up to 2^35-1 = 34359738367 stellations permitting polyhedra with infinite surface area and infinite convex hull.