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  • $\begingroup$ Your solution is absolutely brilliant, especially the second part where you extract the boundary points. Would there be a way to construct a MeshRegion from BDG3, so that I could integrate some field over? Ideally I would have a MRPerfect such that Integrate[Exp[x^2 + y^2 + z^2], {x, y, z} \[Element] MRPerfect] works, and such that BDG3 would be the BoundaryMesh of MRPerfect. $\endgroup$ Commented Sep 22, 2017 at 15:32
  • $\begingroup$ I tried BoundaryDiscretizeRegion[BDG3] which fails. Perhaps Mathematica does not recognise that all points are in a plane. I suspect that one would have to pick a point in the region (say RegionCentroid) and then manually define triangles from there to every boundary point. $\endgroup$ Commented Sep 22, 2017 at 17:02
  • $\begingroup$ @AlexanderErlich BoundaryDiscretizeRegion works only for (n-1)-dimensional MeshRegions embedded in $\mathbb{R}^n$, $n\in \{2,3\}$. "Boundary" in Mathematica tends to mean "topological boundary" rather than "boundary of a manifold". Thus, in its current implementation, you cannot achieve BDG3 == BoundaryMesh[MRPerfect] being true. This is why I defined BDG3 by hand. Use DG3 above as the "interior". $\endgroup$ Commented Sep 23, 2017 at 0:23