Or, if you prefer, Rothphone or Saxorusophone.
I'll mention this, however I'll probably screw it up a few times: it's relatively hard to determine alto or tenor without something to compare it to. I use the G#/C#/B cluster: if there's a lot of distance between that and the top of the bell, it's a tenor. I'd also point you to this picture on Wikipedia.
Also, and no offense to museums, but it's very easy to tell the difference between the Eb baritone and Bb bass.
There was a soprano Rothophone. Here's an ad from Orsi. I'm still trying to determine if the gentleman playing in this video (around 2:14) is playing a soprano Rothophone or a Sax Oboe.