Editing Abstract polytope (section)

===Moduli space===
The group ''G'' of symmetries of a realization ''V'' of an abstract polytope ''P'' is generated by two reflections, the product of which translates each vertex of ''P'' to the next.{{sfn|McMullen |Schulte |2002|pp=140–141}}{{sfn|McMullen|1994|p=231}} The product of the two reflections can be decomposed as a product of a non-zero translation, finitely many rotations, and possibly trivial reflection.{{sfn|McMullen |Schulte |2002|p=141}}{{sfn|McMullen|1994|p=231}}

Generally, the [[moduli space]] of realizations of an abstract polytope is a [[convex cone]] of infinite dimension.{{sfn|McMullen |Schulte |2002|p=127}}{{sfn|McMullen|1994|pp=229–230}} The realization cone of the abstract polytope has uncountably infinite [[algebraic dimension]] and cannot be [[Closed set|closed]] in the [[Euclidean topology]].{{sfn|McMullen |Schulte |2002|p=141}}{{sfn|McMullen|1994|p=232}}