OK, here we go again which was predictable. I'm not classically trained, I'm basically a rock/blues/jazz player starting in the 60's. To me a dim chord when put on a chord chart is a 4 note minor 3rd interval chord, and yes there's only three of them. Never have I seen what is intended as a dim chord written on a chart as a dim7. I would read a Cdim7 as a m7b5 or half diminished. IOW, a dim7 means one flat or dominant mot a double flat. That's because if the author of that chart wanted a standard dim chord it would be written as a Cdim. This is from thousands of fakebook charts I've used over the years. I understand that classically speaking it's a double flat but it's not common usage in my experience which is why I asked what the OP intended.

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