Un-Subdivide treats identical mesh differently (hidden variables)

I decided to post about this here before reporting it as a bug. This is perhaps the weirdest occurrence I’ve encountered since using Blender thus far: A Blender function (un-subdivide) behaves differently for a piece of mesh, compared to other perfectly identical meshes, which implies some kind of hidden variable on the mesh in cause.

My example blend contains two sets of perfectly symmetrical rings: When selecting all and hitting un-subdivide, 3 of them will be decimated from one end, but one will be decimated from the other end. I looked closely at each and every one, and there is no difference I can possibly think of that would cause the upper-left one to be different. It is not the UV map, no double vertices, not the normals (all were recalculated outside), no seams or sharps are marked, no difference in the quad / triangle ratio, no shape keys, no materials.

Test blend file

http://pasteall.org/pic/show.php?id=110870
http://pasteall.org/pic/show.php?id=110871
http://pasteall.org/pic/show.php?id=110872

What I wish to know is what’s different about the mesh that’s being un-subdivided from the other end, and how to remove that difference. I need to fix this for a model I’m working on, so I would appreciate an answer if anyone can take a look. Thank you.

Most likely based on vertex order

Go into top view and in edit mode use Mesh / Sort Elements / View Z Axis and I get the same unsubdivide result for each duplicate


Thank you very much! This has indeed fixed it for me.