A Double Torus, Oriented Vertically

This image is shown with the contour lines only; some manual adjustments caused distortion in the flow lines, so I suppressed them. In any case, I think the contours are of more interest here. The figure-8 is added just no disguise the joins. This surface is obtained by pasting together -- very carefully -- the graphs of the eight functions: w Sqrt[1/2 + w Sqrt[5 - 20*y^2 + w 4*Sqrt[1 - 25*z^2]]/(2*Sqrt[5])], where the w's can be, independently, +1 or -1 (hence 8 choices). Each graph was obtained by the contour-and-flow method, but the flows were erased.