0
$\begingroup$
Region[ImplicitRegion[x/Max[y,z] == Max[y,z]/Abs[y-z] && x+y+z == 1,{x,y,z}], 
 PlotRange -> {{0.001, 0.999}, {0.001, 0.999}, {0.001, 0.999}}]

produces the following graph with gaps and incorrect linear segments: enter image description here

Any advice would be very welcome.

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    $\begingroup$ Does DiscretizeRegion[ImplicitRegion[x/Max[y, z] == Max[y, z]/Abs[y - z] && x + y + z == 1, {{x, 0, 1}, {y, 0, 1}, {z, 0, 1}}], MaxCellMeasure -> {"Length" -> 0.001}, Method -> "MarchingCubes"] do what you want? $\endgroup$
    – J. M.'s torpor
    Jan 31 at 20:07
  • $\begingroup$ Perfect, thank you! $\endgroup$
    – user_xyz
    Jan 31 at 20:11

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