How can I make an Invitation that looks like a Lollipop?

Answer 1

You can buy lollipop sticks in the candy making section of craft stores. Then just make a round invitation from any paper you want, and attach it to the stick with a thin strip across the back, or make a 2-sided one with two circles glued together and the stick sandwiched between.

You could even do a folding one that is attached across the top, and opens up to reveal the information inside.
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Answer 2

Use a real lolly pop, and write really tiny on the stick!