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The dimensions of the spaces of $k$-homogeneous $\mathrm{Spin}(9)$-invariantvaluations on the octonionic plane are computed using results from the theoryof differential forms on contact manifolds as well as octonionic geometry andrepresentation theory. Moreover, a valuation on Riemannian manifolds ofparticular interest is constructed which yields, as a special case, an elementof $\mathrm{Val}_2^{\mathrm{Spin}(9)}$.

$\mathrm{Spin}(9)$-invariant valuations on the octonionic plane