Abstract. We consider AD-type orbifolds of the triplet vertex algebras W(p) extending the well-known c = 1 orbifolds of lattice vertex algebras. We study the structure of Zhu's algebras A(W(p) Am ) and A(W(p) Dm ), where A m and D m are cyclic and dihedral groups, respectively. A combinatorial algorithm for classification of irreducible W(p) Γ -modules is developed, which relies on a family of constant term identities and properties of certain polynomials based on constant terms. All these properties can be checked for small values of m and p with a computer software. As a result, we argue that if certain constant term properties hold, the irreducible modules constructed in [Commun.