# Unexpected black lines on the edge of a RegionPlot3D

I want to create the following 3D solid object, which is an octahedron, cutting by six spheres centered at its vertices.

The code is as:

RegionPlot3D[-2 x + 2 y - 2 z + Sqrt >=
0 && -2 x - 2 y - 2 z + Sqrt >= 0 &&
2 x - 2 y - 2 z + Sqrt >= 0 && 2 x + 2 y - 2 z + Sqrt >= 0 &&
2 x + 2 y + 2 z + Sqrt >= 0 && -2 x + 2 y + 2 z + Sqrt >= 0 &&
2 x - 2 y + 2 z + Sqrt >= 0 && -2 x - 2 y + 2 z + Sqrt >= 0
&& (-(1/Sqrt) - x)^2 + y^2 + z^2 > 1/4 &&
x^2 + (1/Sqrt - y)^2 + z^2 > 1/4 &&
x^2 + y^2 + (-(1/Sqrt) - z)^2 > 1/4 &&
x^2 + y^2 + (1/Sqrt - z)^2 > 1/4 &&
x^2 + (-(1/Sqrt) - y)^2 + z^2 >
1/4 && (1/Sqrt - x)^2 + y^2 + z^2 > 1/4, {x, -1, 1}, {y, -1,
1}, {z, -1, 1}, PlotPoints -> 250, Mesh -> None,
PlotTheme -> "Classic"]


and the output looks like: There are moustache like black lines on the edge. Increase the PlotPoints option to 250 cannot remove it.

Update:

Outputs with BoundaryStyle->None: How can I obtain desired smooth version of the solid? Why such black lines happen?

• Try BoundaryStyle -> None. Jul 27, 2017 at 10:11
• The lines still exist but turn into white or something transparent. Jul 27, 2017 at 10:17
• I've found Regions to be a bit unreliable when they get really thin like that. An adaptive mesh approach, using DiscretizeRegion with an appropriate MeshRefinementFunction could do the trick. Have a look at 105756, and see if it helps. Jul 27, 2017 at 11:10
• Using contourRegionPlot3D[] on this problem gives this. Jul 27, 2017 at 12:52
• Thank you @J.M. , this new function via ContourPlot3D solves my problem. By increasing PlotPoints into 80 or so, the output graph looks pretty good. contourRegionPlot3D is much better than the built-in RegionPlot3D in these aspects if 3D solid model is not needed Jul 28, 2017 at 2:22