Suppose that in a real projective plane a cycle of \(n\) lines is radiating from the vertices of a plane \(n\)-gon. Such a figure is called an \(n\)- ring. If, moreover, this figure is equal to the projection of a ring of faces surrounding a plane \(n\)-gon in 3-space, then it is called an \(n\)- calotte (the spatial figure not being coplanar). The projective condition for an \(n\)-ring to be an \(n\)-calotte is called calotte condition. This calotte condition is now expressed in terms of the Cayley algebra which permits an algebraic description of meet and join in the languae of exterior algebra. The author shows that for \(n \geq 5\) the calotte condition becomes Cayley factorizable when multiplied by \(n-4\) brackets.