**by Akiji Yamamoto, NIRIM, Japan**

All superspace groups for one-dimensionally modulated structures (756 superspace groups, excluding enantiomorphic pairs) are given. These are classified into 6 systems. For publications using this table, the following paper should be cited. Akiji Yamamoto, Acta Crystallographica A52, 509-560, (1996).

Click one of 6 items. The table of each superspace group lists the wave vector, superspace groups, equivalent superspace groups if any, centering translations for the non-primitive lattice, symmetry operations for the (first) superspace group and reflection conditions if any. The symbol is similar to the two-line symbol but instead of the prefix, the wave vector is used.

**Reference**

A. Yamamoto, T. Janssen, A. Janner and P. M. de Wolff, *Acta
Cryst.* A**41** (1985) 528.

**Superspace Groups for Two-dimensionally Modulated Structures**

**by Akiji Yamamoto, NIRIM, Japan**

A provisional list of all (3355) superspace groups for two-dimensionally modulated structures (superspace groups, excluding enantiomorphic pairs) are given. These are classified into 6 systems. For publications using this table, the following paper should be cited. Akiji Yamamoto, Acta Crystallographica A52, 509-560, (1996).

Click one of 6 items. The table of each superspace group lists the wave vector, superspace groups, equivalent superspace groups if any, centering translations for the non-primitive lattice, symmetry operations for the (first) superspace group and reflection conditions if any. The symbol is similar to the one-line symbol in 4D superspace groups but has the pair of wave vectors are used. The symbols .ss., .st. etc. stand for the translation along 4-th and 5-th direction when the rotational part is 2x2 identity matrix. The symbol g represents the glide plane in the 2D internal space.

**Superspace Groups for Three-dimensionally Modulated Structures**

**by Akiji Yamamoto, NIRIM, Japan (added Jun. 20, 2000)**

A provisional list of all (11764) superspace groups for three-dimensionally modulated structures (superspace groups, excluding enantiomorphic pairs) are given. These are classified into 7 systems. For publications using this table, the following paper should be cited. Akiji Yamamoto, Proc. Aperiodic 2000.

Click one of 7 items. The table of each superspace group lists the wave vector, superspace groups, equivalent superspace groups if any, centering translations for the non-primitive lattice, symmetry operations for the (first) superspace group and reflection conditions if any. The symbol is similar to the one-line symbol in 4D superspace groups but has the triplet of wave vectors are used. The symbols .sss., .0st. etc. stand for the translation along 4-th, 5-th and 6-th direction when the rotational part is 3x3 identity matrix. The symbol g represents the glide plane in the 2D internal space.

** Reference**

A. Yamamoto, "Crystallography of Quasiperiodic Structures", *Acta
Cryst.* A52 (1996) 509-560.

A. Yamamoto, "Tward Automatic Analysis of Modulated and Composite
Crystals", *Proc. Aperiodic 2000 to be published.*

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