You kind of expect an icon to fall on his face at some point. But here’s Savion Glover, 21 years after he first appeared on Broadway at age ten in The Tap Dance Kid, continuing to take on new challenges–and meeting them in ways that are inevitably hailed as astounding. The show he’s touring here, Improvography, has received raves since it opened in late 2003 in New York. It features a live band and a troupe of seven other dancers, called Ti Dii, in choreographed ensemble pieces with and without Glover to recorded music. But the real reason to see the show is the star’s handful of lengthy solos, improvised to live jazz by an onstage combo. One of the cool things about this dancer is that he doesn’t project and often doesn’t even seem aware the audience is there; instead you watch him go deep inside himself to call up the music of his tapping. An interview in the New York Times last January (prior to the opening of his latest show, Classical Savion, danced to classical music and also praised to the skies) revealed that the toe-tapping interviewee was listening to Coltrane on headphones hidden by his sweatshirt hood throughout his talk with interviewer Sylviane Gold. He told her he was usually “plugged in”–practicing in his mind whether he’s on an errand or talking on the phone. He also said he hasn’t been in a studio “for practorial purposes” in years. Some guys have all the luck. Or genius. Sat 4/30, 5 and 8 PM, North Shore Center for the Performing Arts, 9501 Skokie Blvd., Skokie, 847-673-6300, $52.