LIT The 8 corners are the 3-bit strings. Edges join corners that differ by one bit, and there are 12. Faces are the 6 choices of fixing one coordinate at an end. 8 − 12 + 6 = 2.
AMBER Euler characteristic is the name of that alternating sum for this convex surface.
WALL The identity is about this polyhedron. It is not a census of the galaxy's spheres.