[Twickel]

Hi
Why are there only 14 bravis lattices and not 28 [ combining 4 centres with 7 crystal systems]. I understand that having equal lattice anglestrumps having a smaller unit cell, but how doo I understand this

e.g why do we have 4 orthrohomic unit cells but only one triclinic cell?

[vex]

http://en.wikipedia.org/wiki/Bravais_lattice#Bravais_lattices_in_3_dimensions

Essentially, if you get to the nitty gritty of the symmetry (and by symmetry I mean in terms of group theory) you can show that there are only 14 symmetrically unique possibilities in 3 dimensions. You may also want to read about space group, which is a lot more specific.

[curiouscat]

Essentially, if you get to the nitty gritty of the symmetry (and by symmetry I mean in terms of group theory) you can show that there are only 14 symmetrically unique possibilities in 3 dimensions. You may also want to read about space group, which is a lot more specific.

Warning: Unless you are strong at that sort of abstract math some of that 3D-symmetry stuff is headspinning. 

Don't expect a simple answer; your question is more profound than you might think. Unfortunately, no easy way to explain it without doing the math.

[cth]

e.g why do we have 4 orthrohomic unit cells but only one triclinic cell?

For example, imagine a body centered triclinic cell and draw the lattice on a piece of paper. From this lattice, by changing the cell parameters a, b, c, α, β and γ, you can determine another different triclinic cell that is smaller and not body centered. Which means, body centered triclinic cells are not minimal, they are not Bravais lattices.

[Twickel]

Hmmm
So listening to thelecture [we have not learnt group theory], the lecturer says. " we do not have plane centered tetragonal cells, because we can make a smaller unit cell which still have 90 degree angles but a smaller volume.

If that is the case surely you can make a smaller orthrombic unit cell with all angles still being 90 degrees, so why do we have 4 types of orthormbic cells

[cth]

If that is the case surely you can make a smaller orthrombic unit cell with all angles still being 90 degrees, so why do we have 4 types of orthormbic cells

No. You could make smaller unit cells, but the angles would not be 90° anymore. As a result, you're loosing symmetry elements.

What works for tetragonal (due to the fact that a=b) does not for orthorhombic (because a is different from b).