An Elementary Connect Fano Plane

Question

I never thought I'd be able to make a connect Fano plane out of chemical elements, since there are so few to choose from. And I was right, but I got really close.
So if you haven't seen previous connect Fano planes, they are very much like a connect wall, except you are given seven words (element names in this case). Your job is to determine seven categories such that the elements and the categories form a Fano plane: each category matches exactly three elements, each element is in exactly three categories, each pair of distinct categories have one element in common, and each pair of elements lie together in one category. Ideally, if you get the categories correct, there will be a final answer that matches all seven categories, but I was only able to get six categories to work...so one of the categories will NOT match the final answer.
Obligatory Fano plane picture:

So here are the elements:
COPPER, GALLIUM, LUTETIUM, POLONIUM, PROTACTINIUM, RUTHENIUM, THALLIUM
Solver Note: I used everything I could think of to come up with categories. Element names, atomic numbers, atomic symbols, physical properties (I cap at high school chemistry, so don't pull out your CRC Handbook), and the periodic table are all fair game.
Good luck!
HINT #1:

HINT #2:

Stiv · Accepted Answer

After a LOT of false trails and dead ends I believe I have FINALLY hit upon the solution!

There is an element which meets 6 of these 7 criteria, as set out by the OP, which is:

And for ease of checking some of the Periodic Table-based criteria, here's a copy of it with the relevant elements highlighted:

hexomino · Answer

Edit: Not the right answer but may serve as a partial as OP has suggested some of the categories match the intended solution (I misread the question before, there is a final answer which should belong to six of the constructed categories).
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chrylis -cautiouslyoptimistic- · Answer

I've been able to come up with a number of categories. Here are three of them as a partial answer (ASCII art because I'm having trouble figuring out the current state of LaTeX tables on SE):

An Elementary Connect Fano Plane

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