Plenty of very nice literature is available on the characterization of f-vectors of simplicial complexes of diverse sorts (results by Billera, Bjoerner, Kalai, Stanley, among others). I mention, as an ...
Exactly what set of mathematical tools (means: set of areas of mathematical knowledge) are appropriate to begin with to analyse (to enumerate face vectors associated with polyhedron, to calculate the ...
Lists of stellations of polyhedrons are given particular rules like in the book The Fifty Nine Icosahedra which follows "Miller's Rules". There seems to be no "correct" ruleset to use, so more ...