Table of 2D Space Groups 1008


The following table gives all 17 2-dimensional space groups together with their nomenclature in LEEDpat. The numbering scheme is identical to that used in the International Tables for X-ray Crystallography (Ref. 5 of the bibliography). The space group type is listed in both full and short notation.

 

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Number         type                    class                              LEEDpat name

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1                    p1                      oblique                           "[ 1]  Oblique p1"

2                    p2                           "                                "[ 2]  Oblique p2"

3                    pm                     primitive rectangular        "[ 3]  Primtv. Rect. pm"

4                    pg                           "                                "[ 4]  Primtv. Rect. pg"

5                    cm                      centered rectangular        "[ 5]  Centrd. Rect. cm"

6                    p2mm (pmm)      primitive rectangular        "[ 6]  Primtv. Rect. p2mm (pmm)"

7                    p2mg (pmg)             "                                "[ 7]  Primtv. Rect. p2mg (pmg)"

8                    p2gg (pgg)              "                                "[ 8]  Primtv. Rect. p2gg (pgg)"

9                    c2mm (cmm)       centered rectangular        "[ 9]  Centrd. Rect. c2mm (cmm)"

10                  p4                      square                            "[10]  Square p4"

11                  p4mm (p4m)            "                                "[11]  Square p4mm (p4m)"

12                  p4gm (p4g)              "                                "[12]  Square p4gm (p4g)"

13                  p3                      hexagonal                       "[13]  Hexagonal p3"

14                  p3m1                       "                                "[14]  Hexagonal p3m1"

15                  p31m                       "                                "[15]  Hexagonal p31m"

16                  p6                           "                                "[16]  Hexagonal p6"

17                  p6mm (p6m)            "                                "[17]  Hexagonal p6mm (p6m)"

 

(3')*                pm                     primitive rectangular        "[3']  Rot. Prim. Rect. pm"

(4')*                pg                           "                                "[4']  Rot. . Prim. Rect. pg"

(5')*                cm                      centered rectangular        "[5']  Rot. . Cent. Rect. cm"

(6')*                p2mg (pmg)        primitive rectangular        "[7']  Rot. . Prim.Rect. p2mg (pmg)"

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* For some superlattices, space groups [3], [4], [5], [7] of the superlattice can appear with two inequivalent orientations of their mirror and glide planes. Examples are p(2x1) or c(4x2) on p6mm. In these cases, LEEDpat includes the rotated groups as [3'], [4'], [5'], [7']. These rotated groups can also be used to rotate the orientation of mirror and glide planes in other situations, where they are equivalent under rotation, e.g. for p(2x1) on p4mm.