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We show that for n ≥ 3 n ≥ 3 there are 3 ⋅ 2 n − 1 3 · 2ⁿ⁻¹ complex common tangent lines to 2 n − 2 2n-2 general spheres in R n R^n and that there is a choice of spheres with all common tangents real.
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Sottile et al. (2002) studied this question.
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