Should a stereo soundstage be 3D or 2D?


I read several people talking about a “3D” soundstage. The main purpose of stereo is to provide left-right separation between different sounds in a recording (a “wide” soundstage). I understand that when properly set up, there is also front-back separation (a “deep” soundstage). So there are certainly two dimensions. Where is the third? Will a stereo system provide up-down separation as well? What is the technical explanation?

Thanks for the help!
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I'm not sure if stereophonic reproduction was ever conceived or designed to provide height cues, but well-set-up, good systems can give some, albeit not as pinpoint or extreme as breadth and depth.  Some speakers are reputed to "do" height better than others; I've had a hard time hearing that.  Find a recording of a flamenco dancer stamping her feet (zapateo) and clicking the castanets high over her head, and report back!!
@twoleftears - I think you are correct, in that the first two channel recordings were by comparison to later recordings simply using the two channels to achieve instrument placement in a single dimension across the image. Then sound engineers discovered instruments could be "located’ in two dimensions, i.e. front to back also.

then some artists, using a technique called phasing, are able to fool us into thinking the sound is behind us.

However, based on my own observations, it would appear that recording two channels very accurately captures the venue acoustics, i.e. those little reverberations and echoes off the ceilings and walls, which seems to "fool" our senses into hearing height. Perhaps height is not the right term, maybe it’s more a "sense of space", in particular, a large space..

So if we can reproduce the recorded signal "accurately" we should be able to recreate the recorded image, complete with its sense of space - yes?.

I’ve only recently become aware of this "effect", thanks to the cables I now have in my system. They are DIY and so over the course of their development, I became increasingly aware of how the details of the venue acoustics improved with each version of the cables and how those reverberations and echoes played a role in recreating the image with amazing reality, i.e. sense of space.

With the advancement in recording technology and the also audio equipment, I believe three dimensional sound using two channels is now a reality. You just need the right gear.

I don’t know if any system is capable of achieving your "Flamenco Challenge", mainly because audio enthusiasts spend a lot of time trying to get rid of reflected sound adn perhaps we need to utilize an element of that. But as we learn more about this hobby I can see a day when your challenge will be a achieved.

If you happen to have the name of such a track - I would be interested hear it on my system, which I believe has an innate sense of space.

Regards - Steve
Thank for the helpful responses, everyone. @williewonka , I like your explanation of how the 3D soundstage provides a “sense of space”. That makes more sense than the speakers providing definite vertical separation. 
I have never been to a live performance (orchestra, acoustic etc) where I perceived front to back cues.

I imagine that any front to back cues that may exist in our systems and recordings has more to do how the recording session was mic'd.  But it is my opinion that is not how live music sounds.
@rodman99999 thanks for the Audio Check link! Just now, I did the LEDR test with my headphones, and I could hear the test tone move up in an arc, in addition to left to right.