Symmetric configuration spaces of linkages

A configuration of a linkage Γ is a possible positioning of Γ in R^d , and the collection of all such forms the configuration space C(Γ) of Γ . We here introduce the notion of the symmetric configuration space of a linkage, in which we identify configurations which are geometrically indistinguishable. We show that the symmetric configuration space of a planar polygon has a regular cell structure, provide some principles for calculating this structure, and give a complete description of the symmetric configuration space of all quadrilaterals and of the equilateral pentagon.