We find a class of minimal hypersurfaces H-k as the zero level set of Pfaffians, resp. determinants of real 2k + 2 dimensional antisymmetric matrices. While H-1 and H-2 are congruent to the quadratic cone x(1)(2) + x(2)(2) + x(3)(2) - x(4)(2) - x(5)(2) - x(6)(2) = 0 resp. Hsiang's cubic su (4) invariant in R-15, H-k>2 (special harmonic SO (2k + 2)-invariant cones of degree >= 4) seem to be new.
QC 20180130