# Difference between a region and its convex hull

I have a volume enclosing a certain region. The region is non-convex, and I calculate its convex hull with the built-in Mathematica function. I want to know the difference between the region and its convex hull. The inbuilt RegionDifference function throws the following error:

BoundaryMeshRegion::bsuncl: The boundary surface is not closed because the edges Line[{... ,<<2390>>}] only come from a single face.

Any help would be appreciated.

(* some preliminaries *)
fn[x_, y_] =
x^2 + y^2 +
2/x^2 (-20 x + 0.4 x^2 + y^2)^2 (1/2 + (
Sqrt[
2] (Cos[(x^2)^(1/4)/Sqrt] -
Cosh[(x^2)^(1/4)/Sqrt]))/((x^2)^(
1/4) (Sin[(x^2)^(1/4)/Sqrt] + Sinh[(x^2)^(1/4)/Sqrt])))
fnLimit[x_, y_] = Limit[fn[x, y], x -> 0]
fnPiecewise[x_, y_] =
Piecewise[{{fn[x, y], x < 0}, {fnLimit[x, y], x == 0}, {fn[x, y],
x > 0}}]

(* the region of interest *)
volToPlot =
ImplicitRegion[
fnPiecewise[x, y] - 100 z <
00, {{x, -300, 300}, {y, -300, 300}, {z, 0, 800}}];
vol = BoundaryDiscretizeRegion[
volToPlot, {{-300, 300}, {-300, 300}, {0, 800}},
MaxCellMeasure -> 1000]

(* Convex hull of the region *)
convexHullVol = ConvexHullMesh[vol]

RegionDifference[convexHullVol, vol]

• "RegionDifference is throwing an error" - what error? Jun 1 at 12:26
• Thanks, @MarcoB. I edited the question. Jun 1 at 12:28