A complete system of inequalities for the diameter, in-, and circumradius in the 3-dimensional Euclidean space
Abstract
We present a complete system of inequalities for the inradius, circumradius, and diameter in the 3-dimensional Euclidean space. To do so, we prove quasiconcavity of the inradius evaluated over n-simplices with a common facet independently of the norm/gauge under consideration.
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