Space groups, symbols and numbers

The 65 chiral space groups for protein crystals (no mirror or inversion operations allowed for asymmetric, chiral, protein motifs) are shown below. There are 165 more space groups, and these are achiral, or ‘‘centrosymmetric’’. They contain ‘‘centers of inversion’’ or ‘‘centers of symmetry’’ which require that the molecule and its mirror image be present in equal numbers in the crystal, or that the molecule itself be centrosymmetric. Neither of these is possible for naturally-occurring proteins. Considering the other 165 achiral space groups that contain mirror or inversion operations, a total of 230 (65+165) space groups is obtained. Again, achiral space groups are not accessible to ordinary protein molecules (biological molecules are enantiomorphous). 


aP (anorthic*)   1                [1,P1]                        abc αβγ

mP (monoclinic)  2                [3,P2]                        abc α=γ=90º β90º
mC                                [5,C2]

oP (orthorombic) 222              [16,P222]                     abc α=β=γ=90º
oC                                [20,C222(1)]
oF                                [22,F222]
oI                                [23,I222] 

tP (tetragonal)  4                [75,P4]                       a=bc α=β=γ=90º
                 422              [89,P422] 
tI               4                [79,I4] 
                 422              [97,I422] 

hP (trigonal)    3                [143,P3]                      a=bc α=β=90º γ=120º
hR                                [146,R3]            
hP               32               [149,P312] 
hR                                [155,R32]  
hP (hexagonal)   6                [168,P6] 
                 622              [177,P622] 

cP (cubic)       23               [195,P23]                     a=b=c α=β=γ=90º 
                 432              [207,P432] 
cF               23               [196,F23] 
cI               23               [197,I23] 
                 432              [211,I432] 

*anorthic: having three unequal crystal axes intersecting at oblique angles; or just call it "triclinic"!