I have a volume enclosing a certain region. The region is non-convex, and I calculate its convex hull with the inbuilt Mathematica function. I want to know the difference between the region and its convex hull. The inbuilt RegionDifference function throws the error "The boundary surface is not closed because the edges.... ". 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[2]] - 
        Cosh[(x^2)^(1/4)/Sqrt[2]]))/((x^2)^(
      1/4) (Sin[(x^2)^(1/4)/Sqrt[2]] + Sinh[(x^2)^(1/4)/Sqrt[2]])))
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]

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[2]] - 
        Cosh[(x^2)^(1/4)/Sqrt[2]]))/((x^2)^(
      1/4) (Sin[(x^2)^(1/4)/Sqrt[2]] + Sinh[(x^2)^(1/4)/Sqrt[2]])))
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]