How to label vertex of a 3D convex hull?

Question

I have the following code to plot a 3d convex hull with 4 corners only.

P[0]={0,0,0};P[1]={1,0,0};P[2]={0,1,0};P[3]={0,0,1};P[4]={-1,-1,-1};P[5]={-1,0,-1};
P[6]={0,-1,-1};
R[1]=ConvexHullMesh[{P[0],P[1],P[2],P[3]}];
face[1]=MeshPrimitives[R[1], "Polygons"];
colors = Opacity[.5, #]& /@ { Green, Blue, Yellow,Red} ;
Graphics3D[{EdgeForm[{Thick, Red}], FaceForm[{Red,Green,Blue,Black}],Transpose@{colors , face[1]}}, 
 PlotRange -> {{-1.2, 1.2}, {-1.2, 1.2}, {-1.2, 1.2}}, Axes -> True, 
 ImageSize -> Large, AxesOrigin -> {0, 0, 0}, 
 LabelStyle -> {12, Bold, Black}, 
 AxesStyle -> Thick, Boxed -> True,AxesLabel->{x,y,z},Epilog -> {Inset[Style["[1,3,2]", 20, Bold], {.2, .8}]}]

In the above plot, the corners are at (0,0,0),(1,0,0),(0,1,0) and (0,0,1). I want to label each corner (for a better view) by attaching the coordinate at the corners. How can it be done? So that when I rotate the 3d plot (using mouse) the labels stay attached to the points it denotes.

Answer 1

I did it with Callouts in a ListPointPlot3D combined with your original Graphics3D using Show:

P[0] = {0, 0, 0}; P[1] = {1, 0, 0}; P[2] = {0, 1, 0}; 
P[3] = {0, 0, 1}; P[4] = {-1, -1, -1}; P[5] = {-1, 0, -1};
P[6] = {0, -1, -1};
R[1] = ConvexHullMesh[{P[0], P[1], P[2], P[3]}];
face[1] = MeshPrimitives[R[1], "Polygons"];
colors = Opacity[.5, #] & /@ {Green, Blue, Yellow, Red};

Show[

 Graphics3D[{EdgeForm[{Thick, Red}], 
   FaceForm[{Red, Green, Blue, Black}], Transpose@{colors, face[1]}}, 
   PlotRange -> {{-1.2, 1.2}, {-1.2, 1.2}, {-1.2, 1.2}}, Axes -> True, 
   ImageSize -> Large, AxesOrigin -> {0, 0, 0}, 
   LabelStyle -> {12, Bold, Black}, AxesStyle -> Thick, Boxed -> True, 
   AxesLabel -> {x, y, z}, 
   Epilog -> {Inset[Style["[1,3,2]", 20, Bold], {.2, .8}]}],

 (* Produce Callouts in a separate ListPointPlot3D *)
 ListPointPlot3D[
   MapThread[
     Callout[#1, ToString@#1, #2, 
       LabelStyle -> {Medium, Black, Background -> White}, 
       CalloutStyle -> White] &,
     {{P[0], P[1], P[2], P[3]}, {Left, Above, Right, Left}}
   ]
  ]
]