Jul 6, 2010 · Abstract:A longstanding problem in rigidity theory is to characterize the graphs which are minimally generically rigid in 3-space.

These methods are based on a controlled sequence of vertex splits, a graph theoretic operation known to take a minimally generically rigid framework to a new ...

Creating a block and hole polyhedron. Moving from a 3-connected planar graph, (a), through selecting faces as blocks and holes, (b), to triangulating the the ...

Jul 6, 2010 · Abstract. A longstanding problem in rigidity theory is to characterize the graphs which are minimally generically rigid in 3-space.

There are also symmetry-isostatic block-and-hole frameworks which are counting-balanced, but not strongly counting-balanced. One example of this type is ...

Nov 2, 2009 · 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 ...

... 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- ...

the abstract block and hole polyhedron is also generically isostatic. Assume that the hole and block can be separated by removing the 3 vertices s, t, u ...

This is a theorem of Gluck [5] and in fact these graphs are minimally 3-rigid (isostatic) in view of their flexibility on the removal of any edge. The vertex ...

When the initial structure is geometrically isostatic, this shows that the swapped structure is also geometrically isostatic, giving the strongest possible ...