It won’t be easy to find a rhyme for “Mathletes” — as in, “You can’t join Mathletes, it’s social suicide!”

But that is the challenge for an all-star team making a musical version of “Mean Girls,” a 2004 cult teen comedy movie. The show is scheduled to have a world premiere production in the fall at the National Theater in Washington, a spokesman for the musical said on Friday.

The creative team includes the comedic writer and actress Tina Fey, who wrote the film’s screenplay; “Saturday Night Live” producer Lorne Michaels, who produced the film and will produce the show with Broadway veteran Stuart Thompson (“The Curious Incident of the Dog in the Night-Time”); and the director Casey Nicholaw (“Aladdin,” “The Book of Mormon”).

Setting to music so many memorable bits of high school banter — “You can’t sit with us,” “That’s why her hair is so big, it’s full of secrets” and “On Wednesdays, we wear pink” — will be the composer Jeff Richmond, who is married to Ms. Fey. Nell Benjamin (“Legally Blonde”) is writing the lyrics. The musical will have a developmental lab in April.