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The blue line occurs at the edge of the function, where ϕ wraps from 2π to 0. We can get rid of it by adding BoundaryStyle -> None: SphericalPlot3D[ Abs[.5 + Sin[2 ϕ]/2] Sin[θ] + Abs[.5 + Sin[2 (ϕ + π/2)]/2] Sin[θ], {θ, 0, π}, {ϕ, 0, 2 π}, PlotStyle -> {Opacity[0.3], Yellow}, BoxRatios -> {1, 1, 1/2}, MeshFunctions -> {#3 &}, ...


3

Euler characteristic Vertices - Edges + Faces for torus equals 0. So you can see that when you have n regular haxagons: 6n/3 - 6n/2 + n == 0 (*each vertex is shared between 3 polygons*) (*each edge is shared between 2 polygons*) is fulfilled for any n. That is why it was relatively easy to do what is done in linked answer. As Szabolcs has pointed ...


2

The OP's simpler mesh has the form mesh (* ElementMesh[{{-0.707107, 0.707107}, {-1., -0.11547}, {-0.707107, 0.707107}}, {HexahedronElement["<" 64 ">"], HexahedronElement["<" 64 ">"], HexahedronElement["<" 64 ">"], HexahedronElement["<" 64 ">"], HexahedronElement["<" 64 ">"], HexahedronElement["<" 64 ">"], ...


1

Let me update Simon's code for Mathematica 10. We no longer need to explicitly load TetGenLink. tetrahedra = Level[MeshPrimitives[DelaunayMesh[data3D], 3], {-3}]; radius[p_] := Sqrt[Area[Circumsphere[p]]/(4 Pi)]; radii = radius /@ tetrahedra; alphashape[rmax_] := Pick[tetrahedra, radii, r_ /; r < rmax] faces[tetras_] := Flatten[ tetras /. {a_, b_, c_, ...



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