change color of the face in a 2D ConvexHullMesh [duplicate]

Question

If I say

tri = ConvexHullMesh[{{0, 1}, {1, 1}, {1, 0}}]

a triangle is rendered in blue. How can I change that color? An answer to an earlier question suggested passing tri, which is actually a BoundaryMeshRegion, to HighlightMesh, like this:

hm = HighlightMesh[tri, {Style[0, PointSize[0.05], Red], 
                         Style[1, Thick, Black],
                         Style[2, Green]}]

That does indeed highlight the vertices as red dots and the edges as black lines; but the triangle is still blue. The Properties list in InputForm[hm] sets the MeshCellStyle of the 2-dimensional cells to green. But perhaps HighlightMesh is not prepared to highlight the top-dimensional face?

Maybe I should be using some different approach?

Answer 1

Perhaps this example could be helpful:

pts = RandomReal[1, {10, 2}];
ch = VoronoiMesh[pts]; mp = MeshPrimitives[ch, 2];
ml = MeshPrimitives[ch, 1];
mpt = MeshPrimitives[ch, 0];
Graphics[Riffle[RandomColor[Length@mp], mp]~Join~{Red, Thick, ##} & @@
     ml~Join~{Blue, PointSize[0.02], ##} & @@ mpt]