Unentangled qubit states

Three dimensional projection of all unentangled states of a two qubit quantum system.

#Background
Consider a qubit in a state a|0> + b|1>, where a^2+b^2=1.
Similarly consider another qubit.

The general state of a two qubit system is represented by the state Ψ=x|00>+y|01>+z|10>+w|11>.

This is a 4 dimensional state. Now, a state is unentangled iff ∃ a,b,c,d s.t. Ψ=(a|0> + b|1>)⊗(c|0> + d|1>).

I wrote a small script to map all the points in the 4-dimensional space where unentangled states occur. On taking a 3D projection of this space the shape turns out to be very cool and interesting, so I decided to 3D print it.

#Code
A MATLAB script to calculate the unentangled states is included. If people are not comfortable with MATLAB (and Octave), I could port the script to python, but generating STL files will be an issue. Let me know if anyone wants me to do it.