1. (xyz) (xyz) (xyz) (xyz)
Space groups
I centering & start from P222
I222
(xyz) (xyz) (xyz) (xyz)
a/2 + b/2 + c/2 translation to body centered
lattice point

2. Space groups I centering & 222 - start from P222
(xyz) (xyz) (xyz) (xyz)
(1/2 + x, 1/2 + y, 1/2 + z) ( 1/2 - x, 1/2 - y, 1/2 + z)
(1/2 - x, 1/2 + y, 1/2 - z) (1/2 + x, 1/2 - y, 1/2 - z)
a/2 + b/2 + c/2 translation to body centered
lattice point
1/2+
1/2-

3. What new symmetry elements arise from translation?
Space groups
I centering & start from P222
I222
What new symmetry elements arise from translation?
a/2 + b/2 + c/2 translation to body centered
lattice point
1/2+
1/2-

4. Space groups I centering & 212121 - start from P212121
a/2 + b/2 + c/2 translation to body centered
lattice point
1/4
1/2 - z
1/2 + z
P212121

5. Space groups I centering & 212121 - start from P212121
a/2 + b/2 + c/2 translation to body centered
lattice point
1/4
1/2 - z
1/2 + z z
- z
What's new?

6. 4i (xyz) (xyz) (xyz) (xyz)
Space groups
Mirrors start with mm2
Pmm2
4i (xyz) (xyz) (xyz) (xyz)

7. Space groups Glides - start with mm2 - substitute glide for mirror
Pbm2
What's new?
4d (xyz) (xyz) (x,y+1/2,z) (x,1/2-y,z)

8. Space groups
Glides & 21s - start with mm add 21, remove mirrors, add glide
1/2+ ?
1/2+
Pna21

9. Space groups
Glides & 21s - start with mm add 21, remove mirrors, add glides
Pna21
1/2+
na ma (b/2+c/2) mb a/ c/2
like 2 (a/2+b/2)