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A dissection of a polygon is obtained by drawing diagonals such that no twodiagonals intersect in their interiors. In this paper, we define a toricvariety of Schr\"{o}der type as a smooth toric variety associated with apolygon dissection. Toric varieties of Schr\"{o}der type are Fano generalizedBott manifolds, and they are isomorphic if and only if the associatedSchr\"{o}der trees are the same as unordered rooted trees. We describe thecohomology ring of a toric variety of Schr\"{o}der type using the associatedSchr\"{o}der tree and discuss the cohomological rigidity problem.