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**a**1,

**a**2,

**a**3 for the body-centered cubic (bcc) Bravais can be chosen as

**a**1=ax

**a**2=ay

**a**3=(a/2)(x+y+z)

or, for instance, as

**b**1=(a/2)(y+z-x)

**b**2=(a/2)(z+x-y)

**b**3=(a/2)(x+y-z)

where x,y,z are unit vectors.

Now I should show that any vector of the form

**R**=n1

**a**1+n2

**a**2+n3

**a**3

where n1,n2,n3 are integers

can be presented as

**R**=m1

**b**1+m2

**b**2+m3

**b**3

where m1,m2,m3 are integers

Do anyone have an idea how I can do this?

Does it help me if I construct reciprocal lattice?

//

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