  Let $\alpha$ be an algebraic integer of degree $d$, which is reciprocal. The
house of $\alpha$ is the largest modulus of its conjugates. We compute the
minimum of the houses of all reciprocal algebraic integers of degree $d$ which
are not roots of unity, say $\mathrm{mr}(d)$, for $d$ at most 34. We prove
several lemmata and use them to avoid unnecessary calculations. The
computations suggest several conjectures. The direct consequence of the last
one is the conjecture of Schinzel and Zassenhaus. We demonstrate the utility of
$d$-th power of the house of $\alpha$.
