# A confusion in the representation of states in $k$-space

In the book "Introduction to Quantum Mechanics" by Griffiths, chapter 5 section 3 (Solids), the author states the following:

...Each intersection point in $k$-space represents a distinct stationary state. Each block in this grid, and hence also each state, occupies an elementary volume in this space.

As I understood, there is one state for every point (intersection), but according the statement above it seems to me that there is one state for every block too! as indicated here:

Isn't this a contradiction?! It's quite evident to me that each block represents 8 states because it contains 8 points (vertices)!

So what did I miss?! any clarification please.