plot_2.nb

(*
  Adapted from http://kaurov.com/wordpress/?p=1246
  Dimensions - min: 1, max: 8
*)

n = 3;

u1[a_, b_] := .5 (E ^ (a + I * b) + E ^ (-a - I * b));
u2[a_, b_] := .5 (E ^ (a + I * b) - E ^ (-a - I * b));

z1k[a_, b_, n_, k_] := E ^ (k * 2 * Pi * I / n) * u1[a, b] ^ (2.0 / n);
z2k[a_, b_, n_, k_] := E ^ (k * 2 * Pi * I / n) * u2[a, b] ^ (2.0 / n);

calabi[x_, y_, z_, \[Alpha]_, t_, c_] := Table[
  With[
    { alpha = \[Alpha] - t },
    ParametricPlot3D[
      Evaluate@{
        Re[z1k[a, b, n, k1]] + x,
        Re[z2k[a, b, n, k2]] + y,
        Cos[alpha] * Im[z1k[a, b, n, k1]] +
        Sin[alpha] * Im[z2k[a, b, n, k2]] + z
      },
      {a, -1, 1},
      {b, 0, \[Pi] / 2}
    ]
  ],
  {k1, 0, n - 1},
  {k2, 0, n - 1}
]

model=Show[calabi[0, 0, 0, 0, Pi / 4, False], PlotRange->All]