In both 3ds Max (which uses a right-handed coordinate system) and Unity (which uses a left-handed coordinate system), the cube map faces labelled "left" and "right" show the view facing the opposite direction. This is not the case with the front, back, up, or down directions.
In 3ds Max, this is in the context of rendering cube map images from a Reflect/Refract map. In Unity, both cube map textures and skyboxes exhibit the same left/right "confusion". Oddly, however, the GUI labels for cube maps indicate that left is the -X direction and right is the +X direction - which is correct in Unity - while skyboxes indicate the opposite (all other axial labels are consistent between the two).
The upshot of this is that cube map images rendered by 3ds Max (which each have a suffix indicating their viewing direction) can be assigned to the texture slots in Unity with the same name and everything will work, but only because both programs label the left view as "right" and vice versa.
The only discussion of this I was able to find online was in a blog post on floored.com (search for "Unity Skybox Weirdness" and it should come up; I'd post a link but I lack sufficient reputation to include more than two). Here's an image from the post that illustrates the issue:
Is there a reason why the left/right axes of cube maps are mislabelled in both of these programs? Although it's trivial to ignore once you're aware of it, it seems like there should be a good (or at least historical) explanation for it, unless it's simply a case of a long-overlooked bug in 3ds Max that the Unity developers decided to accommodate.
Any thoughts would be appreciated!