Actually we can get some information in here.But I'm confuse this phenomenon still:

test = ConvexHullMesh[RandomReal[1, {7, 2}]]

Mathematica graphics



But the same result will not appear this case,

region = BoundaryMesh[DiscretizeRegion[SSSTriangle[3, 4, 5]]]

Mathematica graphics

region /@ {"AdjacencyMatrix", "EdgeLengths"}

Mathematica graphics

I think if the properties of "EdgeLengths" can work normally,it will help a lot to Labeling triangle edges in Mathematica 10.

Note this,please. these region have a same head.

Head /@ {test, region}

{BoundaryMeshRegion, BoundaryMeshRegion}


I think what you are using is an undocumented feature in these region objects, so I wouldn't expect it to work properly.

You can see some of the properties by using:


The list is quite long so I won't be including it here. Now, both of your regions will show "EdgeLengths" as one of the properties, so you clearly see that this undocumented feature is not completely fleshed-out. What's documented though, is the PropertyValue approach (well, partly at least), so let's use it:

PropertyValue[{test, 1}, MeshCellMeasure]
(* {0.261146, 0.694517, 0.406227, 0.339956, 0.576842} *)

PropertyValue[{region, 1}, MeshCellMeasure] (* This gives the length of the sides *)
(* {5., 3., 4.} *)

The 1 means we want the 1-D measure, which is the length of the edges. If you want the area, use 2, etc. One should be able to use PropertyList to obtain possible properties of a region, but this doesn't always work. Even in the "possible issues" section of the documentation for PropertyValue (which only shows example of its use with Graphs), it says:

PropertyValue may return $Failed even when a property value exists:

Then shows an example where this happens. Clearly, even this approach is a work in progress.


On the other hand if you still want to access the undocumented "Properties" of the regions, you can still use the also undocumented approach by calling Graphics`Region`ToMeshObject on the mesh objects e,g.

treg = Graphics`Region`ToMeshObject[region];

Then you can now call "EdgeLengths" and other properties:

treg /@ {"AdjacencyMatrix", "EdgeLengths"}

(* {{{0, 1, 1}, {1, 0, 1}, {1, 1, 0}}, {5., 3., 4.}} *)
  • $\begingroup$ Grateful for your patient explanation.:) $\endgroup$ – yode Apr 17 '16 at 15:55
  • $\begingroup$ @yode. You're welcome. We're all confused about some of the region functions. $\endgroup$ – RunnyKine Apr 17 '16 at 15:59
  • $\begingroup$ I just guess such as Graphics`Region`ToMeshObject maybe give a help,but I don't sure. I remain it open for some time. $\endgroup$ – yode Apr 22 '16 at 7:19

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