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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:

enter image description 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.

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Each block contains 1/8 of 8 vertices, because each vertex also belongs to 8 blocks.

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    $\begingroup$ Aha!! it's similar to the counting of atoms in the cubic Bravais lattice! I got it, thank you so much!! $\endgroup$
    – Samà
    Commented Sep 25, 2017 at 18:39
  • $\begingroup$ @Mr.Weathers I know it's been a few years, but could someone maybe expand on this? I still don't see that there is a 1 to 1 correspondence between blocks and vertices. $\endgroup$
    – Marcel Mazur
    Commented Feb 27, 2021 at 1:03

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