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!
128x128saintsaens_op61
I have always assumed it meant left-right and then some amount of depth, so I took that to be 3 dimensions.  Images not just between the speakers (the left-right-center), but also behind.
@saintsaens_op61
It should be 3D, ie. width, height, and depth.
If the system is properly set up, that is, and the recording is good.

e.g. On your favourite St Saens opus 61 (3rd violin concerto) and with dipole speakers, the violinist is in the room while the orchestra is well behind him and beyond (Vengerov, Philarmonia-Pappano, or Shaham, NYP-Sinopoli), outside the room. Regards
The best way to test your system, for accurate (faithful to whatever’s on your media, at least) sound stage reproduction: https://www.audiocheck.net/audiotests_ledr.php                             Also available, on the following Chesky CD, along with a number of other tests(ie: stage depth, Wood Effect/reverse polarity, etc): https://www.amazon.com/Chesky-Records-Sampler-Audiophile-Compact/dp/B000003GF3    (No doubt, that CD could be found for less, elsewhere)                                        More info, regarding the LEDR test: https://www.stereophile.com/features/772/index.html
+1 what @gregm said.

With the right speakers, room acoustics, components, and let’s NOT forget cables - a good recording will immerse you in the performance and the size of the venue and its related acoustics will will become very apparent.

I have a recording of a single Harmonica being played in a church, with pipe organ in the back ground. The resulting sound "transports you" to the venue complete with reverberations and echoes off the walls and ceilings - it is very 3D.

The venue acoustics start to become even more apparent with higher resolving cables - i.e. IC’s, Speaker and power cables.

Most components and many speakers today have the capability of reproducing those subtle acoustics, but very often it is the cables that are not capable of allowing the extremely delicate signals associated with venue acoustics to be adequately transferred between components and speakers.

Also, much of the "dimension" of a recording can be lost due to noise in the various cables - which impacts the component’s ability to faithfully reproduce L/R channels as recorded, impacting image and therefore the sense of "space"

YES - I am a cable believer :-)

Hope that helps - Steve