The complex Grassmannian manifolds belong to the most interesting examples of (noncommutative) topology and geometry. The lowest example that is not a projective space is the Gr(2,4). I will report on recent observations made in discussion with Franceso D'Andrea, Atul Gothe, Arley Sierra and Kevin Rodriguez with a particular focus on the cell decomposition of Gr(2,4) and the relation of this cell decomposition to noncommutative differential geometry.