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We give new examples of minimal submanifolds of      E 2 n + 1 {{\mathbf {E}}^{2n + 1}}       characterised by having their Gauss map’s image lie in degenerate      S O ( 3 ) SO(3)       orbits of      G p , 2 n + 1 {G_{p,2n + 1}}      , the Grassmannian of      p p      -planes in      E 2 n + 1 {{\mathbf {E}}^{2n + 1}}       (where the action on      G p , 2 n + 1 {G_{p,2n + 1}}       is induced from the irreducible      S O ( 3 ) SO(3)       action on      R 2 n + 1 {{\mathbf {R}}^{2n + 1}}      ). These submanifolds are all given explicitly in terms of holomorphic data and are linearly full in      E 2 n + 1 {{\mathbf {E}}^{2n + 1}}      .

Minimal submanifolds of $E\sp {2n+1}$ arising from degenerate ${\rm SO} (3)$ orbits on the Grassmannian