Geodesic
On configuration spaces of planar pentagons
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part VII, Tome 292 (2002), pp. 120-129

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Algebraic formulas for the Euler characteristic are applied to the topological study of moduli spaces of planar polygons. In particular, a complete description of moduli spaces of planar pentagons is obtained using a computer algorithm for the calculation of the Euler characteristic of algebraic varieties. 
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     author = {G. N. Khimshiashvili},
     title = {On configuration spaces of planar pentagons},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     volume = {292},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_292_a6/}
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G. N. Khimshiashvili. On configuration spaces of planar pentagons. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part VII, Tome 292 (2002), pp. 120-129. http://geodesic.mathdoc.fr/item/ZNSL_2002_292_a6/