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Every Winter Games has its unique moment for every visitor, away from the races and medal podiums, that makes it special.

Going into Sochi's final weekend, I was still missing one. Then I went jogging along the seafront in late morning, watching the glimmering Black Sea, when something caught my eye. Dolphins were breaking the surface with their graceful dips and dives. I never thought I would see the sea mammals within one turn of the head from a Winter Olympic park.

The 1994 Lillehammer Games were special, too. Some nights, you could tumble backward into the snow, watch the magic of the Northern Lights above and feel how nature can make your heart pound. In Nagano four years later, it was sitting in piping hot onsen baths amid rocks in the cold outside, gazing up at the snow-capped mountains around you.

The Turin Games in 2006 were about gastronomy with l'Osteria del Boccondivino outside the city. It represents the heart of the slow food movement, and its panna cotta was to die for. Coming to Vancouver four years later was no better. Instead of sweets, the trays of local oysters made the Olympics away from the Olympics one to remember.

In Sochi, it was the fleeting grace of an animal that made the clement, southern location stand out.

— By Raf Casert — Twitter http://twitter.com/rcasert

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Associated Press reporters are filing dispatches about happenings in and around Sochi during the 2014 Winter Games. Follow AP journalists covering the Olympics on Twitter: http://apne.ws/1c3WMiu