In this paper, we study the connected blocks polytope, which, apart from its own merits, can be seen as the generalization of certain connectivity based or Eulerian subgraph polytopes. We provide a complete facet description of this polytope, characterize its edges and show that it is Hirsch. We also show that connected blocks polytopes admit a regular unimodular triangulation by constructing a squarefree Gröbner basis. In addition, we prove that the polytope is Gorenstein of index 2 and that its h^* h ∗ -vector is unimodal.
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Bruckamp et al. (2024) studied this question.