  A significant range of geometric structures whose rigidity is explored for
both practical and theoretical purposes are formed by modifying generically
isostatic triangulated spheres. In the block and hole structures (P, p), some
edges are removed to make holes, and other edges are added to create rigid
sub-structures called blocks. Previous work noted a combinatorial analogy in
which blocks and holes played equivalent roles. In this paper, we connect
stresses in such a structure (P, p) to first-order motions in a swapped
structure (P', p), where holes become blocks and blocks become holes. When the
initial structure is geometrically isostatic, this shows that the swapped
structure is also geometrically isostatic, giving the strongest possible
correspondence. We use a projective geometric presentation of the statics and
the motions, to make the key underlying correspondences transparent.
