MathDB
max line segment fitting into dodecahedron made by 2 reg. tetrahedra

Source: Netherlands - Dutch MO 1987 p4

December 25, 2022
geometry3D geometrydodecahedrongeometric inequalitytetrahedron

Problem Statement

On each side of a regular tetrahedron with edges of length 11 one constructs exactly such a tetrahedron. This creates a dodecahedron with 88 vertices and 1818 edges. We imagine that the dodecahedron is hollow. Calculate the length of the largest line segment that fits entirely within this dodecahedron.