Hochschild cohomology for nonstandard self-injective algebras of tree class $D_n$

We construct minimal projective bimodule resolutions for nonstandard self-injective algebras of finite representation type. Further, using this resolution we calculate dimensions of the Hochschild cohomology groups and describe Hochschild cohomology algebra in terms of generators and relations. The above resolution, and thus also the Hochschild cohomology of these algebras, are periodic.