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This paper proves explicit formulas for the number of dissections of a convexregular polygon modulo the action of the cyclic and dihedral groups. Theformulas are obtained by making use of the Cauchy-Frobenius Lemma as well asbijections between rotationally symmetric dissections and simpler classes ofdissections. A number of special cases of these formulas are studied.Consequently, some known enumerations are recovered and several new ones areprovided.

Counting symmetry classes of dissections of a convex regular polygon