This system is from a nice collection of algebraic surfaces defined by three variables, found here.

We will use their particular example, called `cube':

x^6 + y^6 + z^6 - 1 = 0

The above Paramotopy input generates the data necessary for the following image. However, since the parameter and variable data are stored separately from each other, the data must be concatenated to display properly in three dimensions.
Stacks Image 17