plotting - How to show well the convexhull in 3d?, for a given set of points

I´m trying with

alfa = 0.75
p = {{1, 0, 0}, {alfa, 0, 1 - alfa}, {alfa, 1 - alfa, 0}, {0, alfa, 
   1 - alfa}, {0, 1 - alfa, alfa}}

chull = ConvexHullMesh[p];

Show[HighlightMesh[chull, Labeled[1, "Index"]], 
 Graphics3D[{Red, Sphere[p, 0.05]}], Axes -> True, Boxed -> True, 
 AxesLabel -> {x, y, z}]

but only create the convexhull of the first 4 points.

I don´t know what´s the problem to create the convexhull with the last.

Answer

If you generate random points using p = RandomReal[{-1, 1}, {5, 3}] then your code works fine -- suggesting that the problem has to do with the fact that all your points lie in a plane. A simple solution is to perturb one of the points slightly outside the plane:

alfa = 0.75;
p = {{1,0,0}, {alfa,0,1-alfa}, {alfa,1-alfa,0}, {0,alfa,1-alfa}, {0,1-alfa,alfa+0.0000001}};    

chull = ConvexHullMesh[p];
Show[HighlightMesh[chull, Labeled[1, "Index"]], 
 Graphics3D[{Red, Sphere[p, 0.05]}], Axes -> True, Boxed -> True, AxesLabel -> {x, y, z}]

enter image description here

Comments

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