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