Misuse of the word triclinic

Some unit cells in the manual are referred to as “triclinic”. This is a misnomer, as the word triclinic is only used for crystal systems and not for unit cells. It refers to the most general arrangement for a periodic lattice (the least symmetrical Bravais lattices). Both the rhombic dodecahedron and the truncated octahedron are instead Wigner-Seitz cells of lattices, and more precisely of the face-centered cubic and of the body-centered cubic lattices respectively. Which, as the name suggests, are both cubic (the most symmetrical Bravais lattices) and not triclinic.

You are correct. But what the manual refers to is that a unit cell like a rhombic dodecahedron can be handled by code which handles general triclinic unit cells. In an MD code there is no point in having a special case for FCC cells (although there have been MD codes that handled the truncated octahedron through tricks using a cubic? unit cell). So the phrasing in the manual could possibly be refined. But I don’t of a good word to indicate all unit cells not having all angles equal to 90 degrees.

There is one more element of confusion here.

It’s “unit cell”.

A unit cell is formed by n vectors in n dimensional space. Even a triclinic one. This means that a three-dimensional unit cell is by definition a parallelepiped. It can not be neither a rhombic dodecahedron nor a truncated octahedron (which instead are parallelohedra).

While we are at rephrasing the wording in the manual, a good idea would be to also replace “unit cell” with “periodic cell”. By doing so, parallelohedra could be listed among the available periodic cells for the simulation to run.

Most of GROMACS only cares about the 3 periodic vectors. So the unit cell if I understood you correctly.
Only visualization tools allow you to output atoms in other periodic cells.

I see. Then we should remove the idea of a rhombic dodecahedral or a truncated octahedral periodic cell. No matter how nice this is. And substitute those with an FCC or a BCC unit cell.
Among other things, BCC is the optimal lattice quantizer in three dimensions (which to me translates into the fact that BCC would outperform - although only slightly - FCC).

No, these are well known concepts in the community and they are useful for visualizing the output.
FCC gives the optimal spherical packing, which results in a rhombic dodecahedron when using what is called the “compact” representation in GROMACS.

I will see if I can clarify the documentation such that it follows official meanings but still mentions all the terms we use now.

I agree with the usefulness of the visualisation of the nearest neighbourhood of a point of a lattice as its Voronoi diagram (or Wigner-Seitz cell if you like). My point is only to dispel any doubt the reader might have about the relation between a polyhedron such as the rhombic dodecahedron and a unit cell. Parallelohedra are just not unit cells.

Indeed the FCC lattice gives the optimal sphere packing. The question is whether the problem of minimising the number of solvent molecules into a periodic cell (or that of saving the most CPU time) translates into the optimal sphere packing problem or instead into something like the optimal sphere covering problem.

It translates to the sphere packing problem. Trust me that the technical aspects are well studied. MD simulations are rather important nowadays and takes a significant fraction of the HPC time world wide. Periodic interactions are by now well understood and optimized. The naming of many aspects of MD can be a mess though.