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ParametricPlot3D[{Cos[y] Cosh[x], Cosh[x] Sin[y], Sinh[x]}, {x, -10, 10}, {y, -10, 10}]
ParametricPlot3D[{Cos[y] Cosh[x], Cosh[x] Sin[y], Sinh[x]}, {x, -10, 10}, {y, -10, 10}]
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