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We construct 2n-2 smooth quadrics in Rn whose equations have the same degree 2 homogeneous parts such that these quadrics have 3⋅ 2n-1 isolated common real tangent lines. Special cases of the construction give examples of 2n-2 spheres with affinely dependent centres such that all but one of the radii are equal, and of 2n-2 quadrics which are translated images of each other.

Configurations of 2 n - 2 Quadrics in R n with 3 · 2 n-1 Common Tangent Lines