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withparadox2

ParametricPlot3D[ {(1 + Cos[v]) Cos[u] + 0.085 Cos[5 u] + (0.994 v/[Pi])^100, (1 + Cos[v]) Sin[u], 6 Sin[v] + 2 Cos[v] - 0.7 Log[1 - v/[Pi]]}, {u, -[Pi], Pi}, {v, -[Pi], Pi}, Mesh -> False, BoxRatios -> 1, PlotStyle -> {Green, Specularity[Yellow, 10]}, ImageSize -> 350]

Then we get:

enter image description here

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