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    $\begingroup$ Try BoundaryStyle -> None. $\endgroup$ Commented Jul 27, 2017 at 10:11
  • $\begingroup$ The lines still exist but turn into white or something transparent. $\endgroup$ Commented Jul 27, 2017 at 10:17
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    $\begingroup$ 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. $\endgroup$ Commented Jul 27, 2017 at 11:10
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    $\begingroup$ Using contourRegionPlot3D[] on this problem gives this. $\endgroup$ Commented Jul 27, 2017 at 12:52
  • $\begingroup$ 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 $\endgroup$ Commented Jul 28, 2017 at 2:22