Why Do Different Primitive Unit Cells for Diamond Look So Different?

[Porkaborg]

TL;DR Summary

Primitive unit cell of diamond, great confusion.

Hi guys , I want to construct a primitive unit cell for diamond, which is made of a fcc lattice and a basis of 2 carbons atoms. I know that a primitive unit cell isn't unique but the two variants I get are drastically different . As far as I can see they both include 2 whole atoms/points in the lattice, however one of them occupies 1/4 of the conventional-cell volume, and the other occupies 1/8 of the conventional-cell volume.

When I couldn't get further in reasoning, I tried googling it and found both versions listed as primitive unit cells for diamond. But I am still confused why they look so very different.
(The left picture doesn't include rest of the atoms for some reason but they are there before creating the primitive unit cell)

I hope someone can point out the difference , or pinpoint why I may be confused, please comment if I need to add some additional info.

 

[DrDu]

How do you want to fill space with only translated copies of a tetrahedron?

 

[Porkaborg]

I guess I can't , which is needed to fulfill the definition of a unitcell. Thanks a lot DrDu!. Upon looking some more at it , the tetrahedron also doesn't include a single lattice point which it is supposed to do to be a primitive unit cell.