# How to memorize 7 crystal systems?

Is there any trick to memorize the angles and sides of 7 crystal systems of crystalline solids?
1. Cubic
2. Tetragonal
3. Orthorhombic
4. Monoclinic
5. Hexagonal
6. Rhombohedral or Trigonal
7. Triclinic

## 1 Answer

The first step is understanding what you have. The seven crystal systems are derived from decreasing symmetry (lifting degeneracies) of the cubic system by altering lengths and angles. Example: Cube volume is $\ce{a^3}$. Parallelepiped volume with all symmetries explicit is

http://www.rockhounds.com/rockshop/xtal/index.shtml
Good reading about crystal systems and their expression.
http://en.wikipedia.org/wiki/Space_group
As usual, nomenclature is a mess.
http://en.wikipedia.org/wiki/Hermann%E2%80%93Mauguin_notation
That's a winner.

Crystallographers often translate the unit cell within the lattice to make its contents "nice." The rhombohedral system is particularly nasty for choosing the unit cell itself. 65 Sohnke space groups of 230 overall contain chiral formula units. Racemic screw axes make that interesting, ${2_1}$, ${4_2}$, ${6_3}$. Within the 65, 11 enantiomorphic space groups - themselves chiral without regard to unit cell contents - allow the same substance to crystallize in two mirror-image space groups.

• For bonus points: There is the monoclinic crystal system (two right angles). Why there is no biclinic crystal system (i.e. a crystal system with one right angle)? Oct 20, 2014 at 2:52
• A triclinic system could have one right angle, but that wouldn't make it more symmetric. Right?
– Karl
Aug 21, 2015 at 20:26