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graphics3d - Labeling distinct objects produced by Show[RegionPlot3D's]



I have these commands


j0=Q1>0&&Q2>0&&Q3>0&&Q1+3 Q2+2 Q3<1;j1=j0&&Q1^2+3 Q2 Q1+(3 Q2+Q3)^2<3 Q2+2 Q1 Q3;Choi=2 Q3+1<2 Q1+3 Q2;MUB=Q1>3 Q2+4 Q3;Show[RegionPlot3D[j1,{Q1,0,1/2},{Q2,0,1/3},{Q3,0,1/4},AxesLabel->{"Subscript[Q, 1]","Subscript[Q, 2]","Subscript[Q, 3]"}],RegionPlot3D[j0&&MUB,{Q1,0,1/2},{Q2,0,1/3},{Q3,0,1/4},AxesLabel->{"Subscript[Q, 1]","Subscript[Q, 2]","Subscript[Q, 3]"}],RegionPlot3D[j0&&Choi,{Q1,0,1/2},{Q2,0,1/3},{Q3,0,1/4},AxesLabel->{"Subscript[Q, 1]","Subscript[Q, 2]","Subscript[Q, 3]"}],RegionPlot3D[j1&&MUB,{Q1,0,1/2},{Q2,0,1/3},{Q3,0,1/4},AxesLabel->{"Subscript[Q, 1]","Subscript[Q, 2]","Subscript[Q, 3]"}]]

which produces a three-dimensional plot


https://www.wolframcloud.com/obj/34c06e57-f136-424f-852a-6c8ad5928b08


I want to label the first (largest) object produced "PPT", the second object, "MUB", and the third object, "Choi". How might I proceed to do so?


Also, I'd appreciate any general recommendations on enhancement/presentation of the plot (coloring,...)



Answer



plots = RegionPlot3D[#, {Q1, 0, 1/2}, {Q2, 0, 1/3}, {Q3, 0, 1/4}] & /@ 
  {j1, j0 && MUB, j0 && Choi};


coords = Cases[#, GraphicsComplex[x_,__] :> Median/@Transpose[x], All][[1]]& /@ plots;
labels = {"PPT", "MUB", "CHOI"};
texts3d = Graphics3D[MapThread[Text, {labels, coords}], Axes -> True];

Show[plots, texts3d, AxesLabel -> (Subscript[Q, #] & /@ {1, 2, 3})]

enter image description here


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