For crystallographic space groups, say, the diamond structure, we have the following information, as described here [1].
The primitive cell lattice vectors can be defined as follows: a1 = (0, 1/2, 1/2), a2 = (1/2, 0, 1/2), a3 = (1/2, 1/2, 0) The translation vectors, can be selected as follows: t0 = (0, 0, 0), t1 = (0, 1/2, 1/2), t2 = (1/2, 0, 1/2), t3 = (1/2, 1/2, 0) The above-mentioned translation vectors can be used to extend the primitive cell to the larger conventional cell, which has the following lattice vectors: b1 = (1, 0, 0), b2 = (0, 1, 0), b3 = (0, 0, 1) It is well known that the above specific set of vectors can be studied by the group theory method, say by lattice [2], or by the groups of vector space (or module) over integers Having said that, I still feel that using such group tools to study the problem described here is quite difficult. Any hints/tips will be highly appreciated. [1] https://en.wikipedia.org/wiki/Unit_cell [2] https://en.wikipedia.org/wiki/Lattice_(group) Regards, HZ -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/5b42a54b-96fe-4e78-aa7e-bdabe04850c5n%40googlegroups.com.
