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I want to draw this region,but the surface is rough.I tried to find options to improve the surface but failed.

Region[RegionIntersection[Cylinder[{{0, 0, -2}, {0, 0, 2}}],
  Cylinder[{{0, -2, 0}, {0, 2, 0}}], 
  Cylinder[{{-2, 0, 0}, {2, 0, 0}}]]]

which gives

enter image description here

besides, PlotPoints -> 200 seems have no place to put.

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Sometimes, it is easier to discretize before intersecting.

BoundaryDiscretizeRegion@RegionIntersection[
  Map[
   BoundaryDiscretizeRegion[#, 
     MaxCellMeasure -> (1 -> 0.05)] &, 
     {Cylinder[{{0, 0, -2}, {0, 0, 2}}], Cylinder[{{0, -2, 0}, {0, 2, 0}}], 
    Cylinder[{{-2, 0, 0}, {2, 0, 0}}]}
   ]
  ]

enter image description here

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ri = RegionIntersection[Cylinder[{{0, 0, -2}, {0, 0, 2}}], 
   Cylinder[{{0, -2, 0}, {0, 2, 0}}], Cylinder[{{-2, 0, 0}, {2, 0, 0}}]];

You can use PlotPoints as a suboption for Method options:

DiscretizeRegion[ri, 
 Method -> {"DualMarchingCubes", PlotPoints -> 150}]

enter image description here

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