color sides in convex Hull

Question

I'm using this code to show the convex hull.

I want to give every sides color because I'm doing some changes in convex hull and I need to see every sides alone.

  ClearAll["Global`*"]
M = x^4 + x y z + y^4 + z^4 + x^2 z^2
p = CoefficientRules[M, {x, y, z}][[All, 1]]
chull = ConvexHullMesh[p];
Show[HighlightMesh[chull, Labeled[1, "Index"]], 
 Graphics3D[{Red, Sphere[p, 0.05], Black, 
   Map[Text[#, # + {0., 0, 0.1}] &, p]}]
   , Axes -> True, Boxed -> True, AxesLabel -> {x, y, z}]

Another step: Can I cut part of the convex hull (or can I just see part of convex hull) because in my work I will just focus on the part from the view from (0,0,0)

Thank you

Answer 1

Mathematica graphics always have a corresponding Graphics or Graphics3D expression. i.e. functions like Plot and ConvexHull don't generate graphics, they generate code. We can take the code and adapt it as required. The code can usually be seen using FullForm, but in this case we also need to use Show:

(gr = chull // Show) // FullForm

Note in the output of the preceding expression the following:

Annotation[
 Polygon[List[List[1, 3, 4], List[3, 5, 4], List[4, 5, 2], 
   List[5, 3, 2], List[3, 1, 2], List[1, 4, 2]]], "Geometry"]

This is clearly the polygons in the figure. (The coordinates are integers which are translated into coordinates by GraphicsComplex, which wraps this expression.) Here is how we can change this expression to color the sides:

gr /. RuleDelayed[
  Annotation[Polygon[polygons__List], "Geometry"],
  Annotation[
   MapIndexed[{ColorData[97, First[#2]], Polygon[#]} &, polygons]]
  ]

The operations that you apply to these polygons are arbitrary. You can also use it to remove planes as what you ask for.