TABLE I
 
        Coordination Sphere Patterns for Triclinic, Monoclinic, and
                         Orthorhombic Space Groups
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Code Sbrtn    Space  Class,       Coordination Sphere Contents              
        NLOW  Group    Z                                                   
          MLOW
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
AA   TA  1  1 P1       T 1   6 I in plane-1,2; 4 I    above; 4 I    below
AB   TA  2  2 P1-bar   T 2   6 I in plane-1,2; 4 C    above; 4 C    below
CA   TC  7  9 P1-bar   T 2   6 I on all axes;  4 C    above; 4 C    below
 
AC   TA  3  3 Pm       M 2   6 I in plane-1,2; 4 P3 - above; 4 P3 - below
AD   TA  3  4 Pc       M 2   6 I in plane-1,2; 4 P3 1 above; 4 P3 1 below
AE   TB  5  6 P2       M 2   6 I in plane-1,3; 4 A3   right; 4 A3   left 
AF   TB  5  7 P21      M 2   6 I in plane-1,3; 4 S3   right; 4 S3   left 
AG   TB  6  8 Pc       M 2   6 I in plane-1,3; 4 P3 2 right; 4 P3 2 left
AH   TA  4  5 P21      M 2   6 I in plane-1,2; 4 S3   above; 4 S3   below
 
AI   FA  8 10 P21/c *  M 4   2 I on axis-3; 4 P3 1; 4 S3; 4 C
AJ   FA  8 11 P2/c  *  M 4   2 I on axis-3; 4 P3 1; 4 A3; 4 C
AK   FA  9 12 P21/c    M 4   2 I on axis-3; 4 P3 1; 4 S3; 4 C
AL   FA  9 13 P2/c     M 4   2 I on axis-3; 4 P3 1; 4 A3; 4 C
AM   FB 10 14 P21/c    M 4   2 I on axis-1; 4 P3 2; 4 S3; 4 C
AN   FC 11 15 P21/m    M 4   2 I on axis-1; 4 P3 -; 4 S3; 4 C
AO   FC 11 16 P2/m     M 4   2 I on axis-1; 4 P3 -; 4 A3; 4 C
FA   FD 30 72 P21/c    M 4   6 I in plane-1,2; 4 C    above; 4 P3 1 below
FB   FD 30 73 P21/m    M 4   6 I in plane-1,2; 4 C    above; 4 P3 - below
FC   FE 31 74 P21/c    M 4   6 I in plane-1,3; 4 S3   right; 4 C    left
FD   FE 31 75 P2/c     M 4   6 I in plane-1,3; 4 A3   right; 4 C    left
 
AP   OA 12 17 P21212   O 4   2 I on axis-3; 4 S1; 4 S2; 4 A3
AQ   OA 12 18 P212121  O 4   2 I on axis-3; 4 S1; 4 S2; 4 S3
AR   OB 13 19 Pnn2     O 4   2 I on axis-3; 4 P1 n; 4 P2 n; 4 A3
AS   OB 13 20 Pna21    O 4   2 I on axis-3; 4 P1 2; 4 P2 n; 4 S3
AT   OB 13 21 Pnn2     O 4   2 I on axis-3; 4 P2 n; 4 P3 n; 4 A1
AU   OB 13 22 Pna21    O 4   2 I on axis-3; 4 P2 n; 4 P3 2; 4 S1
AV   OB 13 23 Pna21    O 4   2 I on axis-3; 4 P1 n; 4 P2 1; 4 S3
AW   OB 13 24 Pba2     O 4   2 I on axis-3; 4 P1 2; 4 P2 1; 4 A3
AX   OB 13 25 Pnc2     O 4   2 I on axis-3; 4 P2 1; 4 P3 n; 4 A1
AY   OB 13 26 Pca21    O 4   2 I on axis-3; 4 P2 1; 4 P3 2; 4 S1
AZ   OC 14 27 P212121  O 4   6 I in plane-2,3; 4 S2; 4 S3
BA   OC 14 28 P21212   O 4   6 I in plane-2,3; 4 S2; 4 A3
BB   OC 14 29 P21212   O 4   6 I in plane-2,3; 4 A2; 4 S3
BC   OC 14 30 P2221    O 4   6 I in plane-2,3; 4 A2; 4 A3
BD   OC 14 31 Pna21    O 4   6 I in plane-2,3; 4 P1 n; 4 S3
BE   OC 14 32 Pnn2     O 4   6 I in plane-2,3; 4 P1 n; 4 A3
BF   OC 14 33 Pna21    O 4   6 I in plane-2,3; 4 P1 2; 4 S3
BG   OC 14 34 Pba2     O 4   6 I in plane-2,3; 4 P1 2; 4 A3
BH   OC 14 35 Pca21    O 4   6 I in plane-2,3; 4 P1 3; 4 S3
BI   OC 14 36 Pnc2     O 4   6 I in plane-2,3; 4 P1 3; 4 A3
BJ   OC 14 37 Pmn21    O 4   6 I in plane-2,3; 4 P1 -; 4 S3
BK   OC 14 38 Pma2     O 4   6 I in plane-2,3; 4 P1 -; 4 A3
 
CB   EA 15 39 Pbca     O 8   2 P1 2; 2 P2 3; 2 P3 1; 2 A1; 2 A2; 2 A3; 2 C
CC   EA 15 40 Pbca     O 8   2 I on axis-1; 4 P1 2; 2 P3 1; 2 A1; 2 A2; 2 C
CD   EB 32 41 Pbcn     O 8   2 P1 2; 2 P2 3; 2 P3 n; 2 S1; 2 A2; 2 S3; 2 C
CE   EB 32 42 Pbcn     O 8   2 I on axis-2, 2 P1 2; 4 P2 3; 2 A2; 2 S3; 2 C
CF   XX XX 43 Pnma     O 8   Programmed only with PLAN line for Z=4
 
DA   NA 16 44 Cc       M 4   6 I in C plane-1,3; 4 P3 2 right; 4 P3 2 left
DB   NA 17 45 C2       M 4   6 I in C plane-1,3, 4 A3   right; 4 A3   left
DC   NA 18 46 C2/c     M 8   4-6 I in C plane-1,3; 3-4 A3; 0-1 P3 2; 4 C
DD   NA 18 47 C2/c     M 8   2 I on C diagonal-1,3, 4 P3 2; 4 A3; 4 C
DE   NA 18 48 C2/c     M 8   2 I on axis-3, 4 P3 2, 4 A3; 4 C
DF   NC 19 49 Fdd2     O 16  Programmed only with AXIS line for Z=8
DG   NC 20 50 Fdd2     O 16  Programmed only with AXIS line for Z=8
 
EA   NB 21 51 ?        O 8   6 I in C plane-1,3, ? P1
EA   NB 21 52 ?        O 8   6 I in C plane-1,3, ? P2
EC   NB 21 53 ?        O 8   6 I in C plane-1,3, ? P3
ED   NB 21 54 ?        O 8   6 I in C plane-1,3, ? A1
EE   NB 21 55 ?        O 8   6 I in C plane-1,3, ? A2
EF   NB 21 56 ?        O 8   6 I in C plane-1,3, ? A3
EG   NB 21 57 ?        O 8   6 I in C plane-1,3, ? C
 
SA   SA 22 58 A-P2     M 1   6 I in plane-1,2; 4 I  - above; 4 I  - below
              or P-Pm
SB   SA 23 59 C-P21/m  M 2   6 I in plane-1,2; 4 X3 - above; 4 X3 - below
SC   SA 23 60 C-P21/c  M 2   6 I in plane-1,2; 4 X3 - above; 4 X3 - below
SD   SB 24 61 C-P21/c  M 2   6 I in plane-1,3; 4 X3 - right; 4 X3 - left
SE   SB 24 62 C-P2/c   M 2   6 I in plane-1,3; 4 X3 - right; 4 X3 - left
 
SF   SC 25 63 A-P21212 O 2   6 I in plane-1,2; 4 X1 - above; 4 X1 - below
SG   SC 25 64 A-P2221  O 2   6 I in plane-1,2; 4 X1 - above; 4 X1 - below
SH   SD 26 65 A-Pnn2   O 2   6 I in plane-1,3; 4 X1 - right; 4 X1 - left
SI   SD 26 66 A-Pba2   O 2   6 I in plane-1,3; 4 X1 - right; 4 X1 - left
SJ   SD 26 67 A-Pma2   O 2   6 I in plane-1,3; 4 X1 - right; 4 X1 - left
SK   SE 27 68 A-Pnc2   O 2   6 I in plane-1,2; 4 X1 - above; 4 X1 - below
SL   SF 28 69 P-Pmn21  O 2   6 I in plane-1,3; 4 X2 - right; 4 X2 - left
SM   SF 28 70 P-Pma2   O 2   6 I in plane-1,3; 4 X2 - right; 4 X2 - left
 
SN   SG 29 71 C-Pbca   O 4   2 I on axis-3; 4 Y1 3; 4 Y2 1; 4 Y3 2
SO   SH 33 76 P-Pnma   O 4   2 I on axis-2; 4 P2 n; 4 S2; 4 C
SP   SH 33 77 P-Pnma   O 4   2 I on axis-1; 4 P2 n; 4 S2; 4 C
SQ   SI 34 78 A-Pbcn   O 4   2 I on axis-2; 4 P2 3; 4 S2; 4 C
SR   SI 34 79 A-Pbcn   O 4   2 I on axis-3; 4 P2 3; 4 S2; 4 C
SS   SI 34 80 A-Pbcn   O 4   2 I on axis-1; 4 P2 3; 4 S2; 4 C
 
ST   SJ 35 81 A-Fdd2   O 8   2 I on axis-3; 4 T13; 2 d; 2 d23; 2 d13; 2 d12
SU   SJ 35 82 A-Fdd2   O 8   2 I on axis-1; 4 T13; 2 d; 2 d23; 2 d13; 2 d12
SV   SK 36 83 C-Pbcn   O 4   2 I on axis-3; 4 Y1 n; 4 X2 1; 4 Y3 2
In Table I, axis-1, axis-2, and axis-3 refer to the Eulerian
rotation axes used in the MOLPAK search routines.  The unique axis (b) of
the monoclinic space groups is along axis-3.  The various symbols have the
following meaning:
 
     Plane-ij is the plane containing axis-i and axis-j
 
     Pi j is a glide plane perpendicular to axis-i with an
           axis-j translation
     P1 n is a glide plane perpendicular to axis-1 with a
           diagonal translation
     Pi - is a mirror plane perpendicular to axis-i
 
     Si   is a two-fold screw axis parallel to axis-i
 
     Ai   is a two-fold rotation axis parallel to axis-i
 
     Xi - is a two-fold axis with the restrictions of a mirror plane
     
     Xi j is a two-fold axis with the restrictions of a glide plane
 
     Yi j is a screw axis with the restrictions of a glide plane
 
     T13  is an identity translated by 1/2 along axis-1 and axis-3
 
     d    is a P1 with a 1/4 glide along all three axes
 
     d23  has an additional translation of 1/2 along axis-2 and axis-3
 
     "above" and "below" refer to directions along axis-3
 
     "left" and "right" refer to directions along axis-2
 
The lead C, A, or P before the space group designations for symmetric
molecules means that the molecule contains an internal center of symmetry,
two-fold axis, or mirror plane.  For example, C-P21/c is the reduced space
group for P21/c containing centric molecules.
 
  *  AI and AJ are special cases of AK and AL respectively, with pairs of
     P3 1 along axis-3.  This allows the MOLPAK search routine to run much
     faster.