Theater and dance figure prominently in the lineup for the 2012 Edinburgh Festival — as does a hard-to-categorize nod to the Olympics.The theater program includes world preems of “Gulliver’s Travels” by Romanian helmer Silviu Purcarete and the Radu Stanca National Theater of Sibiu, and “Wonderland,” a subversive take on Lewis Carroll by Scotland’s Vanishing Point. There’s a rare visit from Ariane Mnouchkine’s Paris-based Theatre du Soleil with four-hour epic “Les naufrages du fol espoir (aurores),” as well as outings from the Suzuki Company of Toga with “Waiting for Orestes: Electra,” Dublin’s Gate Theater with “Watt” (seen earlier in Gotham as part of the Under the Radar fest) and Chile’s Teatro Playa with “Villa” and “Discurso.” There are also three Shakespeares: “2008: Macbeth,” the high-tech TR Warszawa production that was presented by Brooklyn’s St. Ann’s Warehouse in 2008; “A Midsummer Night’s Dream” by Russian helmer Dmitry Krymov; and “The Rape of Lucrece” produced by the Royal Shakespeare Company and starring Camille O’Sullivan, the torch singer who recently played at Joe’s Pub in New York. The fest’s three-week summer program features ten theater companies and seven dance troupes in addition to “Speed of Light,” an unusual performance event involving large numbers of endurance runners moving in choreographed formation over the slopes of Arthur’s Seat, the city’s iconic mountain. Created by Glasgow environmental art company NVA, “Speed of Light” is billed as an artistic response to the London Olympic Games, which will finish just as the Edinburgh Festival begins. Fest topper Jonathan Mills, who was a.d. of the Melbourne Festival at the time of the Sydney Olympic Games, hopes to attract auds and media to the Scottish capital in the gap before the start of the Paralympic Games in late August. With that in mind, he’s hosting the first Edinburgh Culture Summit (Aug. 13 and 14), to be attended by culture ministers from around the world. The politicos will join artists to debate the power of culture to foster international relationships. Alongside the extensive opera program, the dance slate includes a triple bill by Julliard Dance from Gotham’s Julliard School and visits from the Mariinsky Ballet and the Deborah Colker Dance Company. The fest runs Aug. 9-Sept. 2.