We show that the strongly regular graph on non-isotropic points of one type
of the polar spaces of type U(n,2), O(n,3), O(n,5), O+(n,3), and
O−(n,3) are not determined by its parameters for n≥6. We prove this
by using a variation of Godsil-McKay switching recently described by Wang, Qiu,
and Hu. This also results in a new, shorter proof of a previous result of the
first author which showed that the collinearity graph of a polar space is not
determined by its spectrum. The same switching gives a linear algebra
explanation for the construction of a large number of non-isomorphic designs.Comment: 13 pages, accepted in Linear Algebra and Its Application