# ContourPlot3D doesn't show all of the curve

I am studying a polynomial

F[x_, y_, z_] := 2*(x^2 - 2 x*y + y^2 - y*z)^2 - y^4 - z^4.

I tried plotting this: a = ContourPlot3D[F[x, y, z] == 0, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}] But I figured out that the line $$\lambda (1, 1, 1)$$ also lies on my surface, because $$F[\lambda,\lambda,\lambda] = 0$$. However, if I plot that together, it doesn't look like that.

Show[Graphics3D[{Red, Thick, Line[{{-2, -2, -2}, {2, 2, 2}}]}], a] • As I understand it, ContourPlot3D does not show sets of dimension less than two e.g. ContourPlot3D[(x - y)^2 + (y - z)^2 == 0, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}]. May 3 at 16:02
• Thank you! So do you know maybe a way to show also the sets of dimension less than two? May 3 at 16:53
• No, I don't know such a way, expect suggested by you. May 3 at 17:45
• Try RegionPlot3D[-.02 <= F[x, y, z] <= .02, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, PlotPoints -> 100, MaxRecursion -> 4 ] which gives roughly what you expect. May 3 at 20:03

Workaround using RegionPlot3D
F[x_, y_, z_] := 2*(x^2 - 2 x*y + y^2 - y*z)^2 - y^4 - z^4 