- Special p-forms are forms which have components phi_{mu_1...mu_p} equal to +1,-1 or 0 in some orthonormal basis. A p-form phiin Lambda^p R^d is called democratic if the set of nonzero components {phi_{mu_1...mu_p}} is symmetric under the transitive action of a subgroup of O(d,Z) on the indices {1,...,d}. Knowledge of these symmetry groups allows us to define mappings of special democratic p-forms in d dimensions to special democratic P-forms in D dimensions for successively higher P geq p and D geq d. In particular, we display a remarkable nested stucture of special forms including a U(3)-invariant 2-form in six dimensions, a G_2-invariant 3-form in seven dimensions, a Spin(7)- invariant 4-form in eight dimensions and a special democratic 6-form Omega in ten dimensions. The latter has the remarkable property that its contraction with one of five distinct bivectors, yields, in the orthogonal eight dimensions, the Spin(7)-invariant 4-form. We discuss various properties of this ten dimensional form.
