They're as lovely as Ziegfeld girls, as leggy as showgirls, as apple-pie as pom-pom girls, and they inhabit a surreal realm between A Chorus Line and a halftime band (only with T-straps instead of tubas). They make Busby Berkeley's mad tappers look sloppy, and their grueling performance schedule—up to five 90-minute shows per day for almost eight weeks running—requires the stamina of Seabiscuit. They're the fabled Rockettes of Radio City Music Hall, and this year's Christmas Spectacular, November 9 through December 30, marks the 75th anniversary of a show that's like no other on earth.

The act began in 1932 and was soon presented as free entertainment between screenings of the first-run movies playing Radio City Music Hall. Today, the Rockettes are the show, a kick-line calculus that begins with an illusion. A Rockette can be between five feet six and five feet ten and a half, but "on the line" the tallest are in the middle, a trick of perception that evens things up. And though the kick line appears to be linked (a sequined centipede!), the women don't touch. Says one Rockette, a 15-year veteran, "When you have four or five shows a day, and that's maybe 800, 900 kicks, you just have to do it on your own." The result—36 women moving as one, and with the finesse of Fosse dancers—is a stirring sight that sells more tickets in two months than any Broadway hit sells in a year.

"Most companies would have said, 'It's a classic, it works, leave it alone,'" says Jonathan Hochwald, executive V.P. of productions at MSG Entertainment, which produces the show. This company, however, sees the 75th anniversary as perfect timing for a millennial re-invention. New numbers, costumes, technology, grand finale, and even new snow—not to mention a real live double-decker tour bus—all are taken to cutting-edge levels of virtuosity.

Rockette-heads need not worry. The amazingly mathematical Parade of the Wooden Soldiers" (like Balanchine on acid) and the beloved "Living Nativity," a tableau vivant complete with sheep and three camels, both in the show since 1933, remain as historical touchstones. But these, too, have been spruced up. "There's not a moment that we haven't addressed," says Hochwald. "This show's going to have more Rockette numbers than ever—each of them a tour de force."