Geometry: partition of a (0,1) -polytope, why is it adjacent?

There is one thing that I need to understand in this document:
https://link.springer.com/content/pdf/10.1007%2FBF01589099.pdf
(with references to this)

He said that :
Let's call $ P $ a (0,1) -polytope, the convex hull of the vectors in $ X $, where : $ X_i ^ 0 = {x in X: x_i = 0 } $ Y $ X ^ 1_i = {x in X: x_i = 0 } $ is an appropriate partition of $ X $.

As you show that $ X_i ^ 0 $ is adjacent to $ P $ at least one element of $ X ^ 1_i $?