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  • $\begingroup$ Take a look at MeshPrimitives. $\endgroup$ Commented Feb 26, 2016 at 9:13
  • $\begingroup$ that just returns a list of polygons. how do i make say each individual polygon into a new MeshRegion? $\endgroup$ Commented Feb 26, 2016 at 11:07
  • $\begingroup$ You can extract coordinates of MeshRegion with MeshCoordinates, and construct a new mesh regions with each individual cell in MeshCells list from it, but that's a bit excessive. Points, lines, polygons and three-dimensional regions provided by MeshPrimitives should be directly usable in symbolic regions computation, such as a specification of region of integration using Element. $\endgroup$ Commented Feb 26, 2016 at 11:41
  • $\begingroup$ @kirma is right: the primitives returned by MeshPrimitives can be used directly in further computation. However, if you absolutely positively have to have mesh regions, you can use DiscretizeRegion. For example if vm is the output of VoronoiMesh, then DiscretizeRegion /@ MeshPrimitives[vm, 2] will give you a list of mesh regions corresponding to the cells of the Voronoi tessellation. $\endgroup$ Commented Feb 26, 2016 at 11:45
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    $\begingroup$ @kirma Since the original regions are polygons more complex than triangles, they are definitely going to be split into smaller components (i.e. triangular cells). That shouldn't affect the integration though. Also, you may be able to minimize the number of mesh cells by specifying a high MaxCellMeasure value for DiscretizeRegion. $\endgroup$ Commented Feb 26, 2016 at 18:19