ISOSTATIC BAR AND JOINT FRAMEWORKS IN THE PLANE WITH IRREDUCIBLE PURECONDITIONS

If a bar and joint framework in generic position is infinitesimally ri gid with independent edges then we call it isostatic. This paper exami nes when the special positions that make a planar isostatic framework infinitesimally flexible form an irreducible variety. We find an induc tive graph operation, called triangle-free edge splitting, which gener ates irreducible conditions. We introduce minimal isostatic graphs (MI G's), which are isostatic graphs that contain no proper isostatic subg raph. We settle the existence of an MIG for every number of vertices, except for v = 4, 5, 7.