Hi, I am now studying crystall structure and stucked in a question. Any kind of help will be highly appreciated. In crystall structure talking about translational symmetry they said that for any crystall a translational vector of the kind , T = m*a + n*b + p*c where a,b,c are primitive length. and n, m, p are integers, can connect any two lattice points , but my question is if the lattice is of bcc or fcc type how this vector connects any two lattice points in them with taking n,m,p as integers ? Because they will have a lattice point in between the eight corners of the cube, then how can we connect that point (the middle one for body centered cubic) from the corner of the cube by mean of this vector. As taking m,n,p as integers we can go from a corner but not in the middle . Thank You
See "Bravais lattice": http://academic.brooklyn.cuny.edu/physics/tung/GC745S12/vg4-7.pdf And http://physics.unl.edu/tsymbal/teaching/SSP-927/Section 01_Crystal Structure.pdf