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#Edit2#

So now all of the discrete regions vertices lies within the convex body, but the volume enclosed by the mesh is still greater than 22/5.

Edit 2

So now all of the discrete regions vertices lies within the convex body, but the volume enclosed by the mesh is still greater than 22/5.

Edit 3

By the way, in order to have at least on higher resolution picture of the body:

So the vast majority of points lies inside. But few of them loe outside. I guess they deviate so little that this would not matter. Maybe one can move them just a little inside and maybe the volume still stays greater than 22/5?

So the vast majority of points lies inside. But few of them loe outside. I guess they deviate so little that this would not matter. Maybe one can move them just a little inside? For simplicity, I just move all the points of the discrete region a little bit towards the origin:

Mscaled = TransformedRegion[M, {x, y, z} |-> 0.99999999 {x, y, z}];
Count[cf[MeshCoordinates[Mscaled]], 0]
Volume[Mscaled]

0

4.40038

So now all of the discrete regions vertices lies within the convex body, but the volume enclosed by the mesh is still greater than 22/5.

377

1601751

109

399393