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1.
A bikini that is for plus-sized women.
"That girl with the nice body has a nice fatkini!"

"Hey, do you sell fatkinis?"
"What?"
"Do you sell fatkinis? Bikinis for plus-szied women?"
"This is Abercrombie & Fitch, girl, of course we don't."
by Chris's_Zen May 24, 2013
 
2.
A bikini that is designed to be worn by plus size women. It is cut differently than more traditional bikinis so as to make the wearer feel less self conscious about being fat.
"I'm 5'4'' and I weight 250 lbs. I don't think I could ever wear a bikini. I'll just have to stick to a one piece"
"That's not true, try a fatkini."
by VictoriousSecret May 24, 2013