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Rules for the input of a Hermann Mauguin space group symbol

  1. First letter is the Bravais symbol describing translational symmetry of the unit cell (P,A,B,C,R,I,F) followed by a blank (space).

  2. The symmetry operator symbols generating the equipoints in the unit cell follow. They are all separated by a blank - except if a slash combines them (denoting that the symmetry plane is perpendicular to the corresponding symmetry axis). Example : I 4/m m m (not case sensitive)

  3. A screw axis (usually denoted by a subscript following the axis) is entered as two adjacent numbers :
    P 63/M M C, P 21 21 21

  4. An inversion (shown by the bar above the axis) is entered as a minus sign. Example : R -3 C. The exception is the triade in the cubic systems, which is automatically recognized as an inversion in the centrosymmetric groups and thus can be omitted: F D 3 M is ok, and so is F d -3 m.

  5. Settings with origin at center must be used.

  6. Use monoclinic setting with b as unique axis (alpha, gamma = 90.0).

  7. Use obverse hexagonal setting for rhombohedral space groups.


List of recognized Hermann Mauguin Space Group Symbols

Non-enantiogenic (Sohncke) space groups in green, of those the space groups with multiple indexing possibilities in red, and polar space groups with undefined origin in bold red

 TRICLINIC
 P 1          P -1
 MONOCLINIC
 P 2         P 21        C 2         P M         P C
 C M         C C         P 2/M       P 21/M      C 2/M
 P 2/C       P 21/C      C 2/C
 ORTHORHOMBIC
 P 2 2 2     P 2 2 21    P 21 21 2   P 21 21 21  C 2 2 21
 C 2 2 2     F 2 2 2     I 2 2 2     I 21 21 21  P M M 2
 P M C 21    P C C 2     P M A 2     P C A 21    P N C 2
 P M N 21    P B A 2     P N A 21    P N N 2     C M M 2
 C M C 21    C C C 2     A M M 2     A B M 2     A M A 2
 A B A 2     F M M 2     F D D 2     I M M 2     I B A 2
 I M A 2     P M M M     P N N N     P C C M     P B A N
 P M M A     P N N A     P M N A     P C C A     P B A M
 P C C N     P B C M     P N N M     P M M N     P B C N
 P B C A     P N M A     C M C M     C M C A     C M M M
 C C C M     C M M A     C C C A     F M M M     F D D D
 I M M M     I B A M     I B C A     I M M A
 TETRAGONAL
 P 4         P 41        P 42        P 43        I 4
 I 41        P -4        I -4        P 4/M       P 42/M
 P 4/N       P 42/N      I 4/M       I 41/A      P 4 2 2
 P 4 21 2    P 41 2 2    P 41 21 2   P 42 2 2    P 42 21 2
 P 43 2 2    P 43 21 2   I 4 2 2     I 41 2 2    P 4 M M
 P 4 B M     P 42 C M    P 42 N M    P 4 C C     P 4 N C
 P 42 M C    P 42 B C    I 4 M M     I 4 C M     I 41 M D
 I 41 C D    P -4 2 M    P -4 2 C    P -4 21 M   P -4 21 C
 I -4 M 2    P -4 C 2    P -4 B 2    P -4 N 2    P -4 M 2
 I -4 C 2    I -4 2 M    I -4 2 D    P 4/M M M   P 4/M C C
 P 4/N B M   P 4/N N C   P 4/M B M   P 4/M N C   P 4/N M M
 P 4/N C C   P 42/M M C  P 42/M C M  P 42/N B C  P 42/N N M
 P 42/M B C  P 42/M N M  P 42/N M C  P 42/N C M  I 4/M M M
 I 4/M C M   I 41/A M D  I 41/A C D
 TRIGONAL
 P 3         P 31        P 32        R 3         P -3
 R -3        P 3 1 2     P 3 2 1     P 31 1 2   P 31 2 1
 P 32 1 2    P 32 2 1    R 3 2       P 3 M 1     P 3 1 M
 P 3 C 1     P 3 1 C     R 3 M       R 3 C       P -3 1 M
 P -3 1 C    P -3 M 1    P -3 C 1    R -3 M      R -3 C
 HEXAGONAL
 P 6         P 61        P 65        P 62        P 64
 P 63        P -6        P 6/M       P 63/M      P 6 2 2
 P 61 2 2    P 65 2 2    P 62 2 2    P 64 2 2    P 63 2 2
 P 6 M M     P 6 C C     P 63 C M    P 63 M C    P -6 M 2
 P -6 C 2    P -6 2 M    P -6 2 C    P 6/M M M   P 6/M C C
 P 63/M C M  P 63/M M C
 CUBIC (minus sign in front of triade optional)
 P 2 3       F 2 3       I 2 3       P 21 3      I 21 3
 P M 3       P N 3       F M 3       F D 3       I M 3
 P A 3       I A 3       P 4 3 2     P 42 3 2    F 4 3 2
 F 41 3 2    I 4 3 2     P 43 3 2    P 41 3 2    I 41 3 2
 P -4 3 M    F -4 3 M    I -4 3 M    P -4 3 N    F -4 3 C
 I -4 3 D    P M 3 M     P N 3 N     P M 3 N     P N 3 M
 F M 3 M     F M 3 C     F D 3 M     F D 3 C     I M 3 M
 I A 3 D
 

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