 
Summary: On Global Rigidity and Universal Rigidity of
Generic Bar Frameworks with Few Vertices
A. Y. Alfakih
Department of Mathematics and Statistics
University of Windsor
Windsor, Ontario N9B 3P4
Canada
June 19, 2009
AMS classification: 52C25, 05C62, 15A57
Keywords: Bar frameworks, global rigidity, universal rigidity, Gale transform,
stress matrices.
Abstract
Gale transform was successfully used to classify polytopes with few vertices;
that is, rdimensional polytopes with r + k vertices, where k is small. In this
paper, we use Gale transform to classify rdimensional generic bar frameworks
with r + k vertices, where k 4; as universally rigid, globally rigid or non
globally rigid.
1 Introduction
A configuration p in Rr is a finite set of points p1, . . . , pn whose affine hull is Rr.
Gale transform is a wellknown technique in polytope theory for representing a
