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I have a set of inequalities that plot to the region given below, how do I find the analytical apexes that shape this region?

Reg = RegionPlot3D[
  1 >= a >= b >= 1 - b >= 1 - a >= 0 && 
  1 >= δ >= a - δ >= b - δ >= 1 - a - b + δ >= 0, 
  {a, 1/2, 1}, {b, 1/2, 1}, {δ, 0, 1},
  PlotPoints -> 200, MaxRecursion -> 10]

region

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1 Answer 1

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The region is surrounded by four planes:1 - x - y + z = 0, x = y, 1 - x - 2 y + 2 z = 0 and x = 2 z. We can find the crossover points of them.

Show[Reg, 
 Graphics3D[{PointSize[Large], Red, 
   Point[{x, y, z} /. 
     Catenate[
      Solve[#, {x, y, z}] & /@ 
       Subsets[{1 - x - y + z == 0, x == y, 1 - x - 2 y + 2 z == 0, 
         x == 2 z}, {3}]]]}]]

enter image description here

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  • $\begingroup$ Thanks for the help! $\endgroup$
    – 2ub
    Sep 24, 2017 at 6:16

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