Bill, If you translate your surface to put the singularity at the origin, and also extend it through the origin to make it inversion-symmetric, ParametricPlot3D[{t Cos[2 u] (3 + Cos[3 u]), -t (3 + Cos[3 u]) Sin[ 2 u], 4 t + t Sin[3 u]}, {u, -\[Pi], \[Pi]}, {t, -1, 1}] you get a ruled surface whose lines all pass through the origin (a curve in projective space). -Veit

On May 4, 2020, at 7:55 PM, Bill Gosper <billgosper@gmail.com> wrote:

Does this thing <http://gosper.org/verycrosscap.png>have a name? —rwg

ParametricPlot3D[{(1 - t) Cos[2 u] (3 + Cos[3 u]), (t - 1) (3 + Cos[3 u]) Sin[2 u], 4 t + (1 - t) Sin[3 u]}, {u, -π, π}, {t, 0, 1}, ViewPoint -> Below] _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun