Henneberg Surface
ParametricPlot3D[{ 2 * Sinh[u] * Cos[v] - 2 * Sinh[3 * u] * Cos[3 * v] / 3, 2 * Sinh[u] * Sin[v] - 2 * Sinh[3 * u] * Sin[3 * v] / 3, 2 * Cosh[2 * u] * Cos[2 * v] }, {u, .35,.85}, {v, -π,π}, PlotPoints -> {10, 60}]
ParametricPlot3D[{ 2 * Sinh[u] * Cos[v] - 2 * Sinh[3 * u] * Cos[3 * v] / 3, 2 * Sinh[u] * Sin[v] - 2 * Sinh[3 * u] * Sin[3 * v] / 3, 2 * Cosh[2 * u] * Cos[2 * v] }, {u, .35,.85}, {v, -π,π}, PlotPoints -> {10, 60}]