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I have defined three regions, Slice1, Slice2 and Slice3.

Slice1 = 
  Polygon[{{0, 0}, {1, 0}, {1, 1/(Sqrt[3])}, {1/2, Sqrt[3]/2}}];
Slice2 = 
  Polygon[{{0, 0}, {-1, 0}, {-1, 1/(Sqrt[3])}, {-1/2, Sqrt[3]/2}}];
Slice3 = 
  Polygon[{{0, 
     0}, {-1/2, -Sqrt[3]/2}, {0, -2/Sqrt[3]}, {1/2, -Sqrt[3]/2}}];

CombinedSlice = RegionUnion[Slice1, Slice2, Slice3];
RegionPlot[CombinedSlice, AspectRatio -> Automatic]

When I RegionPlot the combined plot, Slice3 does not have correct boundaries. The boundary shows up correctly when I plot Slice3 individually.

enter image description here

I am using Mathematica 12.0

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  • $\begingroup$ It looks like a bug in RegionUnion[ in cases where we have disjoint regions or regions that have no interior point in common: Try e.g.: CombinedSlice = RegionUnion[Slice1, Slice2]; However, if we have some interior common points: Slice4 = Polygon[{{-0.001, -0.50}, {0.001, -0.5}, {0.001, 0.1}, {-0.001, 0.1}}]; RegionPlot[CombinedSlice, AspectRatio -> Automatic] it works as expected. $\endgroup$
    – Daniel Huber
    Apr 1 at 8:24
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Such bug also appear in 12.2. We had to draw the boundary and interior separately.

Show[RegionPlot[{RegionBoundary@CombinedSlice}, 
  BoundaryStyle -> Red],
 RegionPlot[CombinedSlice, BoundaryStyle -> None]]

enter image description here

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  • $\begingroup$ BTW, can this affect the result if I numerically integrate a function over the whole region? Is it a good idea to integrate over the individual regions and add them? $\endgroup$
    – Archisman Panigrahi
    Apr 1 at 8:51
  • $\begingroup$ @ArchismanPanigrahi It doesn't affect the result. For example, {CombinedSlice // Area, Integrate[1, {x, y} \[Element] CombinedSlice], ArcLength[RegionBoundary@CombinedSlice], 3*ArcLength[RegionBoundary@Slice1] // N} $\endgroup$
    – cvgmt
    Apr 1 at 9:04

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