It’s not often you can say a dance company is performing a genuine service. But the Joffrey Ballet is doing just that with its reconstructions of Vaslav Nijinsky’s unique and prescient works: The Afternoon of a Faun, Jeux, and The Rite of Spring. They were universally reviled when they were first performed, even by his collaborators–neither Debussy, the composer for the first two pieces, nor Stravinsky, from whom the Rite of Spring score was specially commissioned, made any secret of the fact he disliked Nijinsky’s choreography. And the Ballets Russes dancers forced by impresario Sergey Diaghilev (Nijinsky’s lover) to perform these “ugly” pieces let Nijinsky know they hated them. The opening of The Rite of Spring at the Theatre de Champs-Elysees in 1913 caused a riot “so great,” Joan Acocella writes in her introduction to The Diary of Vaslav Nijinsky, “that the dancers could not hear the music. Nijinsky stood in the wings, sweat coursing down his face, screaming the musical counts to the performers.” A downward spiral ensued for the choreographer, who as a dancer had been so popular it’s said fans snuck into his dressing room to steal his underwear. His relationship with Diaghilev deteriorated, after which he married a woman he’d known for four weeks, and then Diaghilev fired him. Five years later Nijinsky descended into the madness that kept him a near vegetable for the remaining three decades of his life. Nijinsky’s story is well-known to balletomanes, but they seldom have the opportunity to see his revolutionary work. The Joffrey hasn’t done The Rite of Spring here since 1987, when it was performed after 15 years of painstaking reconstruction. And Jeux (“Games”), about a flirtatious tennis match, has reportedly never been seen in the United States. All three make up the first of two Joffrey programs this fall. Auditorium Theatre, 50 E. Congress, 312-902-1500; 312-922-2110, ext. 4, for groups of ten or more. “The Nijinsky Mystique” opens Thursday, October 11, 7:30 PM. Through October 14: Friday-Saturday, 2 and 7:30 PM; Sunday, 2 PM. “Arpino and Friends” (artistic director Gerald Arpino’s Reflections and Light Rain and the world premieres of works by Julia Adam and Chicagoan Paul Christiano) opens Thursday, October 18, 7:30 PM. Through October 21: Friday-Saturday, 2 and 7:30 PM; Sunday, 2 PM. $29-$69.