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A pun used to describe the time spent when you and your lover are snuggling, wrapped up in each others arms, facing each other. Like how a koala hugs onto a tree. You are usually really super in love if you spend koalaty time together.
Guy: "I can't wait to see my girl later -- we're going to spend some serious koalaty time together."

Other Guy: "Man, you guys must be in love! She's total wifey material, I'm happy for you guys."
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