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We find a class of minimal hypersurfaces    H  k    as the zero level set of Pfaffians, resp. determinants of real    2  k  +  2    dimensional antisymmetric matrices. While    H  1    and    H  2    are congruent to the quadratic conex  1  2   +   x  2  2   +   x  3  2   −   x  4  2   −   x  5  2   −   x  6  2   =  0    resp. Hsiang's cubic    su   4invariant in    R  15   ,    H   k  >  2(special harmonic    S  O   2  k  +  2    ‐invariant cones of degree ⩾4) seem to be new.

New minimal hypersurfaces in R APTARABOLDITALIC ( k + 1 ) ( 2 k + 1 ) and S APTARABOLDITALIC 2 k 2 + 3 k