Editing Stellation (section)

===Other rules for stellation=== 
Miller's rules by no means represent the "correct" way to enumerate stellations.  They are based on combining parts within the [[stellation diagram]] in certain ways, and don't take into account the topology of the resulting faces.  As such there are some quite reasonable stellations of the icosahedron that are not part of their list – one was identified by James Bridge in 1974, while some "Miller stellations" are questionable as to whether they should be regarded as stellations at all – one of the icosahedral set comprises several quite disconnected cells floating symmetrically in space.

As yet an alternative set of rules that takes this into account has not been fully developed. Most progress has been made based on the notion that stellation is the reciprocal or dual process to [[facetting]], whereby parts are removed from a polyhedron without creating any new vertices. For every stellation of some polyhedron, there is a [[Duality (mathematics)|dual]] facetting of the [[dual polyhedron]], and vice versa. By studying facettings of the dual, we gain insights into the stellations of the original. Bridge found his new stellation of the icosahedron by studying the facettings of its dual, the dodecahedron.

Some polyhedronists take the view that stellation is a two-way process, such that any two polyhedra sharing the same face planes are stellations of each other. This is understandable if one is devising a general algorithm suitable for use in a computer program, but is otherwise not particularly helpful.

Many examples of stellations can be found in the [[List of Wenninger polyhedron models#Stellations: models W19 to W66|list of Wenninger's stellation models]].