= Complex cobordism ring of the quaternionic projective plane
{title2=$MU^*(\mathbb{HP}^2)\cong MU^*(\mathrm{pt})[q]/(q^3),\quad |q|=4$}
For the <quaternionic tautological line bundle> regarded as a complex rank-two bundle, take $q=c_2^{MU}$. Its ordinary image generates degree-four integral cohomology, and its square generates degree eight. The <Atiyah-Hirzebruch spectral sequence> collapses because the cells have dimensions $0,4,8$ and the coefficients are even. The classes $1,q,q^2$ lift a free basis of the associated graded module, and $q^3=0$ because the theory is connective and the space has dimension eight.
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