The real moment-angle complex of a polygon and necklace sequences (Q2929707)

The real moment-angle complex of an \(n\)-gon is an orientable closed surface of genus \((n-4)2^{n-3}+1\). It admits an action of the product of the dihedral group \(D_{2n}\) associated to the polygon with \({\mathbb{Z}}_2\). In two previous papers [Adv. Appl. Discrete Math. 10, No. 2, 109--119 (2012; Zbl 1288.55005)] [ibid., 121--134 (2012; Zbl 1288.55006)] the author computed the integer homology of the orbit spaces of the actions of four specific subgroups of \(D_{2n}\times {\mathbb{Z}}_2\). These results are summarized in this paper, and additionally the integer homology of the orbit space under the full action of \(D_{2n}\times {\mathbb{Z}}_2\) is computed.