Editing Stellation (section)

===Miller's rules===
In the book ''[[The fifty nine icosahedra|The Fifty-Nine Icosahedra]]'', J.C.P. Miller proposed a [[The fifty nine icosahedra#Miller's rules|set of rules]] for defining which stellation forms should be considered "properly significant and distinct".

These rules have been adapted for use with stellations of many other polyhedra. Under Miller's rules we find:
* There are no stellations of the [[tetrahedron]], because all faces are adjacent
* There are no stellations of the [[cube]], because non-adjacent faces are parallel and thus cannot be extended to meet in new edges
* There is 1 stellation of the [[octahedron]], the [[stella octangula]]
* There are 3 stellations of the [[dodecahedron]]: the [[small stellated dodecahedron]], the [[great dodecahedron]] and the [[great stellated dodecahedron]], all of which are Kepler–Poinsot polyhedra.
* There are 58 stellations of the [[icosahedron]], including the [[great icosahedron]] (one of the Kepler–Poinsot polyhedra), and the [[Second stellation of icosahedron|second]] and [[Final stellation of the icosahedron|final]] stellations of the icosahedron.  The 59th model in ''The fifty nine icosahedra'' is the original icosahedron itself.

Many "Miller stellations" cannot be obtained directly by using Kepler's method. For example many have hollow centres where the original faces and edges of the core polyhedron are entirely missing: there is nothing left to be stellated. On the other hand, Kepler's method also yields stellations which are forbidden by Miller's rules since their cells are edge- or vertex-connected, even though their faces are single polygons. This discrepancy received no real attention until Inchbald (2002).