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


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

enter image description here

Good reading about crystal systems and their expression.
As usual, nomenclature is a mess.
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.

  • $\begingroup$ 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)? $\endgroup$ – Abel Friedman Oct 20 '14 at 2:52
  • $\begingroup$ A triclinic system could have one right angle, but that wouldn't make it more symmetric. Right? $\endgroup$ – Karl Aug 21 '15 at 20:26

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.