Thanks, this thread just got started.
I have tumbled fluorite, but, not calcite yet. Photo #6 is actually Mexican Fluorite in Quartz matrix--difficult to tumble due to the varying hardness (Mohs 4 Fluorite, Mohs 7 Quartz). All steps post shaping were done in my Vibratory tumbler (UV-18), vibe tumblers are relatively gentle on the stones.
I have larger pieces of Chinese fluorite, but, they have quartz banding in them. I don't trust that they would tumble well. I did borrow a friends $6000 diamond wheel cabbing machine to shape a few of them (shown below). Don't think I will ever convince my gf to let me get one of those machines...unless I win the lottery...even then, maybe not....
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