6 research outputs found
The combinatorial geometry of stresses in frameworks
In this paper we formulate and prove necessary and sufficient geometric conditions for existence of generic tensegrities in the plane for arbitrary graphs. The conditions are written in terms of "meet-join" relations for the configuration spaces of fixed points and non-fixed lines through fixed points
GEOMETRIC CRITERIA FOR REALIZABILITY OF TENSEGRITIES IN HIGHER DIMENSIONS
In this paper we study a classical Maxwell question on the existence of
self-stresses for frameworks, which are called tensegrities. We give a complete
answer on geometric conditions of at most -valent tensegrities in
both in terms of discrete multiplicative 1-forms and in terms of
"meet" and "join" operations in the Grassmann-Cayley algebra
Geometric criteria for realizability of tensegrities in higher dimensions
In this paper we study a classical Maxwell question on the existence of self-stresses for frameworks, which are called tensegrities. We give a complete answer on geometric conditions of at most -valent tensegrities in both in terms of discrete multiplicative 1-forms and in terms of "meet" and "join" operations in the Grassmann-Cayley algebra