In the classification of simple Lie algebras over the reals, several isomorphisms occur between algebras of small rank in different families. In particular, the real forms of the algebras of rank 3 and type A or D provide such examples. On the level of corresponding linear groups, some of these isomorphisms show up as homomorphisms from special unitary groups (of hermitian forms of Witt index 0,2,1 on a complex vector space of dimension 3, respectively) either onto connected components of orthogonal groups (of Witt index 0,2 on a real vector space of dimension 6) or the unitary group of a suitable hermitian form on a quaternionic vector space of dimension 3. In the latter case, the form is hermitian with respect to a non-standard involution on the quaternions. We construct the pertinent homomorphism via an isomorphism of incidence structures (namely, suitable polar unitals in complex projective space and the quaternion plane, respectively). This approach works well for all suitable ground fields (such that quaternion fields exist) as long as the characteristic is different from 2. Link to the seminar webpage for more information - https://www.wwu.de/AGKramer/index.php?name=TSSS23&menu=teach&lang=de