Hochschild cohomology of algebras of dihedral type. VIII. The Hochschild cohomology algebra for the family $D(2\mathcal B)(k,s,0)$ in characteristic $2$

We describe the Hochschild cohomology algebra for algebras of dihedral type in the subfamily of the family $D(2\mathcal B)$, for which the parameter $c$ is equal to $0$. In the calculation of multiplication in this cohomology algebra, we use the minimal bimodule projective resolution for the algebras under consideration that was constructed in the previous paper of the authors. The obtained results allow us to describe the Hochschild cohomology algebra also for algebras in the family $D(2\mathcal A)$ for which $c=0$.