After reading Madeleine L'Engle's "Ring of Endless Light" as a preteen, I have always imagined that touching a dolphin (or a whale- any cetacean really) would be like touching something wet, smooth and dusty. L'Engle described the skin of a dolphin as smooth, but so soft that it leaves almost a residue on ones hands.
As someone who is weird about odd textures, I have to say that I wouldn't advise touching a whale, either. It sounds like a nightmare.
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