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I understand that you want the vertex coordinates of the triangles used to plot the surface. If this were the case, the following code exemplifies how to get the list of such coordinates:

var("x,y,z")
surf = implicit_plot3d(x^4+y^4+z^4==1,(x,-1,1),(y,-1,1),(z,-1,1))
surf.triangulate()
surf.vertex_list()