Emmet: Limestone, rectangular cut on the back of his right hand. Jackhammer-y weapon.
Rex: “Dolomite”, actually just another Limestone w/ his gem flipped over to have the point up (to hide the cracks!). He also has a jackhammer, but keeps knuckle dusters in his gem.
He’s the original Limestone, but due to his gem being damaged and Red Diamond not knowing how to heal gems, he gets swiftly replaced with a copy of him with the exact same memories but no capacity for growth. So people assume Emmet just stagnates during the timeskip between the two movies - no, it’s because he’s a rushed copy! Rex is very much not happy about being replaced.
Lucy: Fluorite, teardrop cut over her heart. Hammer! Since her gem is fluorescent, she’s got lots of flashy colors.
Benny: A Peridot, but dyed blue, inverted triangle cut over his chest, like where the Classic Space logo is on his suit! He’s got cleats he can hook onto his boots, as well as a laser gun given to every Peridot assigned to a space station. His gem is cracked a little bit. Squads of five Peridots all dyed different colors are assigned to space stations!
Cosmo: Part of a previous squad that got replaced by Benny’s squad after disaster struck. His gem is over his right eye and cracked much worse. Same weapons, but the gun is upgraded to a cannon he can socket inside of a limb extender he uses as a prosthetic arm.
Unikitty: A corrupt but relatively tame Tiger’s Eye. Her gem is a heart cut and on her forehead, and her weapon is a lance that manifests as a big horn she can project out of her gem when corrupt. She can also produce fire!
Vitruvius: An off-color Sapphire, being green instead of blue. His gem is slightly cracked and on the back of his head. He can’t see, so he can’t exactly perceive his future visions very well, but he’s... very good at guessing what happens in them. His weapon is a staff.
Batman: An Onyx with bat-shaped boomerang weapons because of COURSE. His gem is on his chest and kind of ovular, so kind of where the Batman symbol would be on his outfit.
Good Cop / Bad Cop: A Red and Blue Pearl. When the red side is out, it’s Bad Cop, and the gem is nestled in his right palm. When the blue side is out, it’s Good Cop, and the gem is nestled in his left palm. He’s got a gun! Scribble is stuck between both colors and the gem is just... wherever.
Lord Business: Red Diamond, in the usual five-sided diamond cut and on his upper chest like the knot of a tie. He has a Rejuvenator handy at all times, in case his Pearl steps out of line. And, unfortunately, what causes his Pearl to step out of line is his treatment of them, so...
Powers: A Red and Blue Pearl, that was replaced by GCBC after being shattered. But he got reconstructed by rebels! So he’s severely cracked and unstable, but hides his gem in his back. He’s got limb extenders keeping his limbs together and uses blasters in the hands as weapons. And the usual gun.