Abstract
We construct 2n-2 smooth quadrics in R n whose equations have the same degree 2 homogeneous parts such that these quadrics have 3⋅ 2 n-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.
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Megyesi Configurations of 2 n - 2 Quadrics in R n with 3 · 2 n-1 Common Tangent Lines. Discrete Comput Geom 28, 405–409 (2002). https://doi.org/10.1007/s00454-002-0744-9
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DOI: https://doi.org/10.1007/s00454-002-0744-9