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Mutually tangent spheres in $n$-space. (English)
Math. Mag. 88, No. 2, 146-150 (2015).
Summary: In this note we prove that the points of tangency of $n + 1$ mutually tangent spheres in $n$-dimensional space lie on a generalized sphere. Coxeter’s observation that for each of five mutually tangent spheres there is a sphere passing through the six points of mutual contact of the remaining four is a corollary of this result in the $n = 3$ case.
Classification: G40
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