  In 1992, Brehm and K\"uhnel constructed a 8-dimensional simplicial complex
$M^8_{15}$ with 15 vertices as a candidate to be a minimal triangulation of the
quaternionic projective plane. They managed to prove that it is a manifold
"like a projective plane" in the sense of Eells and Kuiper. However, it was not
known until now if this complex is PL homeomorphic (or at least homeomorphic)
to $\mathbb{H}P^2$. This problem was reduced to the computation of the first
rational Pontryagin class of this combinatorial manifold. Realizing an
algorithm due to Gaifullin, we compute the first Pontryagin class of
$M^8_{15}$. As a result, we obtain that it is indeed a minimal triangulation of
$\mathbb{H}P^2$.
