You may find here some examples of algebraic surfaces plotted with
implicit3D and plot3D.
If you click on a small image, you will have the menu of the plotter with the
equation of the surfaces already loaded. Which will allow you to plot a
bigger image of the surface, while playing with the parameters (colors,
viewing angles, zoom, spin, etc).
Demo
Equation
Description
x2+y2-z2=0
Quadratic cone.
x2+y2+z2+2xyz=1
Cubic with 4 singular points.
x4+y4+z4+5xyz=0
A quartic surface with 4 branches touching at the origine.