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6

The OP's updated example The OP's example exhibits some numerical problems about which the fastidious ToElementMesh and even some System functions complain. Since the OP is dealing with the System` Region* functions to produce graphics, I'll assume the warnings can be ignored as long as the functions do not fail. There are two things that lead to problems ...


3

I don't know of a built-in way to get a periodic boundary. New answer Another way: One potential drawback is that the tetrahedra are aligned with a regular grid. But if the main goal was to increase the fineness of the mesh near the center, then this is a way to do that. First create a hexahedral mesh of an appropriate fineness along the boundary. Then ...


5

The problem is that PolyhedronData["DodecahedronIcosahedronCompound"] consists of an intersecting dodecahedron and icosahedron: PolyhedronData["DodecahedronIcosahedronCompound"] /. Polygon[p_] :> {Opacity[0.6], Riffle[{Red, LightBlue}, Polygon /@ SplitBy[p, Length]]} A fix is to cut out the middles of the faces of the dodecahedron and ...


0

I got a reply from Mathematica indicating that it is a numerical precision issue (the Mathematica implementation of the convex hull seems to work at a lower precision than the data types used). Two work arounds are: Scale the data by a large number Approximate the data by rationals In other words, use PlotPolytope2[n_] := Module[{V = 1000 ...


5

Shorter, though undocumented: Graphics[{LightBlue, EdgeForm[Black], MeshPrimitives[vm, {2, "Interior"}]}, ImageSize -> 720]


7

EDIT New Answer Using the RegionBounds and IntersectingQ functions we can easily achieve this. First we collect the cells of the Voronoi diagram and compute their region bounds, then comparing with that of the overall Voronoi diagram we can select the interior polygons. (* vm is the Voronoi diagram of your image *) cells = MeshPrimitives[vm, 2]; (* cells ...


7

First, it would seem there is a fair amount to say. On the other hand, there is even more not to say, as this shows all the unimplemented properties (both regions give the same result): mr = DiscretizeRegion@Disk[]; (* mr = DiscretizeRegion@ImplicitRegion[1/4 <= x^2 + y^2 <= 1, {x, y}] *) Pick[mr["Properties"], Quiet@Check[mr[#], Missing[#]] ...



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