Symmetric configuration spaces of linkages

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