Unified treatment of multisymplectic 3-forms in dimension 6

On a 6-dimensional real vector space $V$ there are three types of multisymplectic 3-forms. We present in this paper a unified treatment of these three types. Forms of each type represent a subset of ${\mathrm{\Lambda }}^3{V}^{\ast }$. In two cases they are open subsets, in the third one it is a submanifold of codimension 1. We study the geometry of these subsets.