Given a simple graph $G$, the graph associahedron $P_G$ is a convex polytope whose facets correspond to the connected induced subgraphs of $G$. Graph associahedra have been studied widely and are found in a broad range of subjects. Recently, S. Choi and H. Park computed the rational Betti numbers of the real toric variety corresponding to a graph associahedron under the canonical Delzant realization. In this paper, we focus on a pseudograph associahedron which was introduced by Carr, Devadoss and Forcey, and then discuss how to compute the Poincaré polynomial of the real toric variety corresponding to a pseudograph associahedron under the canonical Delzant realization.
Suyoung CHOI. Boram PARK. Seonjeong PARK. "Pseudograph and its associated real toric manifold." J. Math. Soc. Japan 69 (2) 693 - 714, April, 2017. https://doi.org/10.2969/jmsj/06920693