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