Super stable tensegrities and the Colin de Verdière number ν <math xmlns="http://www.w3.org/1998/Math/MathML" altimg="urn:x-wiley:03649024:media:jgt23188:jgt23188-math-0001" wiley:location="equation/jgt23188-math-0001.png"><mrow><mrow&

Abstract A super stable tensegrity introduced by Connelly in 1982 is a globally rigid discrete structure made from stiff bars and struts connected by cables with tension. We introduce the super stability number of a multigraph as the maximum dimension that a multigraph can be realized as a super stable tensegrity, and show that it equals the Colin de Verdière number minus one. As a corollary we obtain a combinatorial characterization of multigraphs that can be realized as three‐dimensional super stable tensegrities. We also show that, for any fixed , there is an infinite family of 3‐regular graphs that can be realized as ‐dimensional injective super stable tensegrities.