Her ballet flat is the No.1 selling shoe for Nike-subsidiary Cole Haan.

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One new company, CitiSoles, started by two New York University students, Susie Levitt and Katie Shea, offers a new twist: A ballet flat with a rubber sole that splits in the center, making it easier to fold and tuck into a zippered pouch, which also unfurls into a tote for carrying high heels home at night.

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Round-toed ballet pumps, by the way, don't enter the new flat equation.

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Mr. Graham shows me a ballet step with fins, the legs moving outward in opposite directions, the feet flat, slowing the ascending diver, turning the body from side to side to see the reef.

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