Regular Morley tetrahedra from $p$-secting planes
Morley's theorem says that the adjacent angle trisectors of a triangle meet in the vertices of an equilateral triangle. Tran carried the construction to a tetrahedron by trisecting its six dihedral angles and, more generally, by $p$-secting planes, with one parameter $e,f,g>1$ for each pair of opposite edges; the resulting tetrahedron is denoted $\mathcal M_{e,f,g}(ABCD)$. Tran showed that a regular Morley tetrahedron does not force the original tetrahedron to be regular, observed that in his examples some pair of opposite edges has four equal cross edges, and conjectured that this happens…
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