[oaksoft]

A cubic unit cell is described as having minimum symmetry of four 3-fold rotation axes.
I know what 3-fold symmetry is and I can see the axes on a cubic unit cell.

What I'm unsure about is the precise meaning of "minimum symmetry" in the context above.
I want to use that definition to understand how to deduce the minimum symmetry of other unit cell types such as tetragonal and orthorhombic.
Obviously I can simply look them up but I'm trying to understand how to derive them myself.

So.....does anyone know what is meant by minimum symmetry?

[AWK]

Cubic groups can also show 2-fold, 4-fold axes and planes

[cth]

"Minimum symmetry" covers the symmetry elements that are present in every space groups of a given crystal system (cubic for example).

In the case of cubic systems, they all have four 3-fold rotation axes along the cube diagonals. These can define a cubic space group.

But for example not all cubic space groups have 4-fold rotation axes. So you can't use 4-fold axes to define cubic space groups, as it would be too restrictive.


If you look at the space groups list (http://en.wikipedia.org/wiki/Space_group, large table near the end of the page) for the cubic crystal system, you can see that all and every cubic space group has 3-fold axes (examples: P23, P432, Pm-3m,...).

[oaksoft]

"Minimum symmetry" covers the symmetry elements that are present in every space groups of a given crystal system (cubic for example).

In the case of cubic systems, they all have four 3-fold rotation axes along the cube diagonals. These can define a cubic space group.

But for example not all cubic space groups have 4-fold rotation axes. So you can't use 4-fold axes to define cubic space groups, as it would be too restrictive.


If you look at the space groups list (http://en.wikipedia.org/wiki/Space_group, large table near the end of the page) for the cubic crystal system, you can see that all and every cubic space group has 3-fold axes (examples: P23, P432, Pm-3m,...).

I'm afraid we've not had anywhere near enough lectures on this stuff for me to be able to understand that table yet but your bit about a cubic unit cell not always having 4 fold symmetry helps a bit (although I can't imagine an example where it wouldn't).

Thanks for helping.

[cth]

You can have a look at this website http://www.unioviedo.es/qcg/d-MolSym/.

There, you can find this picture (and more) of a cubic symmetry without 4-fold rotation axes:


In green are 2-fold rotation axes and in yellow are 3-fold rotation axes. No other symmetry elements.