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

x^2*y*z +x*y^2+y^3+y^3*z- x^2*z^2 = 0

Just like for the cube example, the above Paramotopy input for the Solitude system 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