A canonical bijection between the set of extreme points of the comass-unit sphere \(S_{2,2k}^* \subset \Lambda^2 (\mathbb{R}^{2k})\) and the manifold of orthogonal complex structures in \(\mathbb{R}^{2k}\) is described, under which unitary bases correspond to decompositions of the forms realizing the conjugate norm of the mass. This correspondence is used for obtaining a classification of faces of the sphere \(S_{2,n}^*\) and the known classification of faces of the set polar to \(S_{2,n}^*\). Bibliography: 10 titles.