Id like to make groups for the different faces of this structure you can see above, and then assign different colours to the faces. Would appreciate any help on how to group them and colour them efficiently.
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Your Problem seems to be linked Object Data. You need to make your Objects Local first and regroup them. First to make them local press U > "Object and Data", while all objects are selected. Then select your group that should always have the same color and press Ctrl+L > "Object Data" to group them.
I think you can make your life a lot easier, by going one step back.
Split the faces of your octahedron apart by selecting the parts in Edit Mode and the hitting P and Separate by Selection.
Then you can generate your spheres on top of the separate polygons with the Duplication Option in the Object Tab from your last question. Creating a mesh on any object, duplicating the mesh and editing faces
That way, you do not have to manually select from a huge number of intersecting objects.