I don't think anybody has yet mentioned the work done on symmetry in VN
by our List-Editor Emeritus, Don Johnson. See his chapter on Look
at the Harlequins in his Worlds in Regression, which
discusses the very prominent symmetry issues in that novel with
reference to Martin Gardener's The Ambidextrous Universe (which,
readers will remember, cites "Pale Fire" and is in turn cited in Ada.)
-Stephen Blackwell