TITLE: Interesting implicit surfaces in $\mathbb{R}^3$
QUESTION [28 upvotes]: I have just written a small program in C++ and OpenGl to plot implicit surfaces in $\mathbb{R}^3$ for a Graphical Computing class and now I'm in need of more interesting surfaces to implement!
Some that I've implemented are:

Basic surfaces like spheres and cylinders;
Nordstrand's Weird Surface;
Klein Quartic;
Goursat's Surface;
Heart Surface;

So, my question is, what are other interesting implicit surfaces in $\mathbb{R}^3?$
P.S.: I know this is kind of vague, but anything you find interesting will be of use. (:
P.P.S: Turn this into a community wiki, if need be.

REPLY [3 votes]: I like this "tetrahedron":

$$
x^4 + 2x^2y^2 + 2x^2z^2 + y^4 + 2y^2z^2 + z^4 + 
8xyz - 10x^2 - 10y^2 - 10z^2 + 20 = 0.
$$
The Entzensberger star:

$$
400(x^2y^2+ y^2z^2+ x^2z^2) = {(1-x^2-y^2-z^2)}^3.
$$
On the higher space forum you can find amazing implicit surfaces, especially those of the member ICN5D. These are 3D slices of surfaces in higher dimension. I reproduced some of them with Python, like this one:

Solid Möbius strip, introduced in this paper: