xmin := 0
xmax := 2*Pi
ymin := -0.35
ymax := Pi
ro[t_, p_] := 
      If[p > 0, 1 - Cos[p], -Sin[Max[p, -0.25]]]
phi[t_, p_] := If[p > -0.35, p, 0]
xxx[t_, p_] := ro[t, p]*Sin[phi[t, p]]*Cos[t]
yyy[t_, p_] := ro[t, p]*Sin[phi[t, p]]*Sin[t]
zzz[t_, p_] := ro[t, p]*Cos[phi[t, p]]
ParametricPlot3D[{yyy[t, p], -xxx[t, p], zzz[t, p]}, {t, xmin, 
        xmax}, {p, ymin, ymax}, PlotPoints -> {21, 31}]