On the circumradius of a special class of n-simplices

Details On the circumradius of a special class of n-simplices On the circumradius of a special class of n-simplices

2010-07-09

arxiv.org/abs/1007.1602v2

Mathematics

Metric Geometry

11 pages

Scientific paper

An n-simplex is called circumscriptible (or edge-incentric) if there is a sphere tangent to all its n(n + 1)/2 edges. We obtain a closed formula for the radius of the circumscribed sphere of the circumscriptible n-simplex, and also prove a double inequality involving the circumradius and the edge-inradius of such simplices. Among this inequality settles affirmatively a part of a problem posed by the authors.

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