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Exactly what it says on the tin I created two polyhedra that I think look very nice, and would like to create a compound of them. Is there any way to do so in Stella that I am unable to find, or some other tool I can use?

You can use the "Edit->Put Model in Memory" submenu to pick a slot to save it to (or keyboard shortcut "m"). Then load other model. Then combine them with "Edit->Add/Blend from Memory".

If they have the same symmetry, then they should align well. If not, your milage may vary.