Periodic boundary condition - 26 translated images

Hi all,

Could someone please help explain why each rhombic dodecahedron simulation box (unit cell) is surrounded by 26 translated images?

I’ve tried, but still failed to visualize the arrangement of these periodic boxes.
Should there be 12 boxes instead, since a rhombic dodecahedron has 12 faces, and 26 sides.

Thanks a lot,
Anh T. Mai

Where have you read about it being 26?

The GROMACS manual notes it is 12, and this visualisation shows that it is 12 as well.

Rhombic dodecahedron has 12 faces, 24 edges and 14 vertices.

Hi Dr_DBW,
Thanks for your reply.
The animation of the visualization is great.
Yes, 12 faces, 24 edges and 14 vertices. I was wrong and miscounted the edges (the sides).

Originally, I read it from the GROMACS Documentation, Release 2019, by Dec 31, 2018 (the .pdf version of the manual).

It’s also written in the online manual page that you shared, the last paragraph,
“Each unit cell (cubic, rectangular or triclinic) is surrounded by 26 translated images. A particular image can therefore always be identified by an index pointing to one of 27 translation vectors and constructed by applying a translation with the indexed vector (see Compute forces). Restriction (5) ensures that only 26 images need to be considered.”

Yes, thanks for pointing out the statement as “Each of the 12 image cells is at the same distance.” (in the paragraph right after the box). I didn’t pay close attention to it.

By the way, the angle between ab, of the rhombic dodecahedron (xy-square), should be 90 degrees, right? I found in another version of the manual, it was noted as “90” degrees.

Many thanks,