FMF - Friends of Minerals Forum, discussion and message board

[Kelldon]

I have been shown a question that I am suppose to know and understand and need some help. I understand the basic concepts but can't seem to picture them correctly. I am a studing geologist but minerals are my low point and apparently this is something I just can't picture.

1. If a particular mineral has only pyramid forms how can the adjacent faces be related (mirrors, x-fold-rotation etc.)

2. What crsytal class can they belong to.

3How the logic order and sturcture of three two or one Hermann-Mauguin symbols used in the tertragonal crystal system.

4. Finally what crystal class can a mineral with rhombic cleavage belong.

[Carles Curto]

Firs of all it is not clear if you are talking about a single pyramid (but I suppose you talk about the more common dipyramid. The second previous note is that to explain some usual concepts on Crystallography is not easy when we haven’t images, then is not always easy to understand the explanations
I think a good solution to a best understood of Crystallography is to have a lot of images and explanations on a good book of elementary Mineralogy (as the Sinkankas one) or Crystallography, for example: Smith, J.R. 1991. Understanding Crystallography. Rochester Mineralogical Symposium. Fairfax, VA. USA (LCCN 91-092990). But now I’ll intent to answer your direct questions.

Distribution of faces on a crystal (not only pyramid) usually is consequence, on tetragonal system, mainly of a quaternary rotation axis, just the vertical one. Then, every face of a concrete form (a pyramid or a dipyramid on your case) is repeated every 90 degrees around that axis. Some other actions, as vertical planes of symmetry and horizontal axis can be added and concretely, if we talk of dipyramid, there is a horizontal plane of symmetry.

Hermann-Mauguin symbols depend of the figure. The single pyramid is an hemiedry and it is Ditetragonal Pyramidal (4mm) while in the case of dipyramid ii is Ditetragonal Dipyramidal (4m / 2m / 2m).
The used symbols correspond to the “actions” of the different elements of symmetry, then, and for all, systems (being X the quantity of elements):
m is 1-fold axis parallel to a mirror plane
X is a single rotation axis (in this case X number indicates the category, 2, 3, 4 or 6, 4 in the case of tetragonal system).
‾X is an inversion axis (alone). (X number indicates the category, 2, 3, 4 or 6, 4 in the case of tetragonal system)
X/m a rotation axis parallel to a plane of symmetry
Xm a rotation axis parallel to a plane of symmetry
Xmm a rotation axis with two parallel planes of symmetry

And the last question (about rhombic cleavage), It depends if rhombic is the form of the cleavage plane (simply the shape) or the structural consequence of the fracture. Think that a rhombic shape of a plane can belong to monoclinic crystals, even a deformed (laterally flattened) tetragonal crystal can have an apparently rhombic section.