# Anybody have time to answer a simple question?

Stephanie Wukovitz sebab at ucla.edu
Wed Dec 13 22:35:34 EST 1995

```In article <4amoae\$1r1s at mercury.cc.uottawa.ca>, Stuart Reid
<g567621 at danis.uottawa.ca> wrote:
>         I was hoping somebody could tell me why a unit cell cannot be
simultaneously A and B-centered, but not C-centered.
>                                 - a Confused Physical-Biochem Student

OK, you  can think of this as being a result of the fact that there is no
way to orient such a (nonexistent)
cell such that it "looks" like part of a primitive lattice.  More specificallyr:

Here's an argument to show that you can't have the "lattice" you propose:

Assume you can.  You are then allowed the translations (0,0,1),(0,1,0),
(1,0,0),(-1,0,0), etc., translations by
multiples of a unit cell.  You are also permitted (0,1/2,1/2), (1/2,0,1/2)
and so forth (the centering on two faces)
You may *not* have the translation (1/2,1/2,0), which represents centering
on a third face.

However, (0,1/2,1/2) + (1/2,0,1/2) + (-1,0,0) = (1/2,1/2,0).  This is
centering on the third face, which we said
was not allowed!  Therefore we do not have a lattice.

Hope this helps!

--
Stephanie Wukovitz
steph at newton.mbi.ucla.edu
UCLA Dept. of Biomathematics/Molecular Biology Institute (Yeates lab)

```