# RegionBoundary of a regular polygon in 3D

For a regular Polygon in 3D I would expect some Line regions for the boundary

poly = Polygon[{{1, 0, 0}, {1, 1, 1}, {0, 0, 1}}];
SimplePolygonQ[poly] (* True*)

boundary=RegionBoundary[poly]


but I get a Polygon-object

boundary = Polygon[{{1, 0, 0}, {1, 1, 1}, {0, 0, 1}}, {1, 2, 3}]

Expecting a one dimensional region RegionMeasure evaluates to my surprise

RegionMeasure[boundary,1] (* \[Infinity]*)
RegionMeasure[boundary,2] (*  Sqrt[3]/2 *)


My questions

Why RegionMeasure[boundary,1] doesn't give the correct length of the boundary?

Shouldn't RegionMeasure[boundary,2] be undefined?

Is there a simple way to get Line-objects as boundary

Thanks

• Region /@ {#, RegionBoundary[#]} &@Disk[] works as one would expect.
– Syed
Nov 10, 2023 at 17:24
• Same with Polygon[{{0, 0}, {1, 0}, {0, 1}}] // RegionBoundary Nov 10, 2023 at 17:28
• Perimeter@boundary works. Maybe it is looking for a 3D region with some volume to it. RegionDimension@poly being 2 might have something to do with it.
– Syed
Nov 10, 2023 at 17:50

I found that only RegionPlot3D can recognize its boundary.
poly = Polygon[{{1, 0, 0}, {1, 1, 1}, {0, 0, 1}}];

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