Kenta Kobayashi, A recursive formula for the circumradius of the n-simplex,
Forum Geometricorum, 16 (2016) 179--184.

Abstract. We present a recursive formula which gives the circumradius of the n-simplex in terms of the circumradius of its facets. Our formula shows that the circumradius of the n-simplex is closely related to the distances from each vertex to the circumcenter of the opposite facet. In particular, our formula shows that the circumradius of the tetrahedron can be expressed by the areas of the pedal triangles of each facet. We could only prove the formula for n <= 5, but numerical results strongly suggest that our formula holds true for any n.

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