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BMT 2015 Geometry Tiebreaker #3

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August 12, 2023
geometry3D geometryanal

Problem Statement

The permutohedron of order 33 is the hexagon determined by points (1,2,3)(1, 2, 3), (1,3,2)(1, 3, 2), (2,1,3)(2, 1, 3), (2,3,1)(2, 3, 1), (3,1,2)(3, 1, 2), and (3,2,1)(3, 2, 1). The pyramid determined by these six points and the origin has a unique inscribed sphere of maximal volume. Determine its radius.
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