Two-dimensional space groups with sevenfold symmetry

1986 ◽  
Vol 42 (1) ◽  
pp. 55-56 ◽  
Author(s):  
A. L. Mackay
Keyword(s):  
Dimensional Space ◽  
Symmetry Groups ◽  
Two Dimensional ◽  
Space Groups ◽  
Symmetry Operations

Fivefold and sevenfold symmetry operations are, of course, incompatible with repetition by a lattice but, with the appearance of structures involving curved sheets, they and other non-crystallographic operations must now be taken into consideration as possibilities of non-Euclidean crystallography develop. Here are described the symmetry groups which might be called 732 and 73m and which may be found in two-dimensional manifolds.

Q-reducible two-dimensional space groups and layer groups

1987 ◽  
Vol 20 (7) ◽  
pp. 1655-1659 ◽  
Author(s):  
D B Litvin ◽  
V Kopsky
Keyword(s):  
Dimensional Space ◽  
Two Dimensional ◽  
Space Groups ◽  
Layer Groups

Group Cohomology and Quasicrystals I: Classification of Two-Dimensional Space Groups

2004 ◽  
Vol 305 (1) ◽  
pp. 37-40 ◽  
Author(s):  
BENJI N. FISHER ◽  
DAVID A. RABSON
Keyword(s):  
Dimensional Space ◽  
Group Cohomology ◽  
Two Dimensional ◽  
Space Groups

Extension of three-dimensional space-group generators to the (3+1) case

1999 ◽  
Vol 32 (3) ◽  
pp. 452-455
Author(s):  
Kazimierz Stróż
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Space Group ◽  
Space Groups ◽  
Symmetry Operations ◽  
Three Dimensional Space

A method of building up the generators of 775 (3+1)-dimensional superspace groups is proposed. The generators are based on the conventional space-group generators selected by Wondratschek and applied in theInternational Tables for Crystallography(1995, Vol. A). By the method, the generation of (3+1) space groups is found to be easier, the description of symmetry operations is closer to that used for the conventional space groups, and ambiguities in the (3+1) group notation are avoided.

REPRESENTATIONS OF SPACE GROUPS

1961 ◽  
Vol 39 (6) ◽  
pp. 830-840 ◽  
Author(s):  
I. V. V. Raghavacharyulu
Keyword(s):  
Dimensional Space ◽  
Irreducible Representations ◽  
Group Method ◽  
Two Dimensional ◽  
Space Group ◽  
Space Groups ◽  
Solvability Property ◽  
Representations Of Space

The construction of the irreducible representations of space groups by the little-group method making use of their solvability property is discussed. As an example the two-dimensional space group p4g is considered and all the allowable representations for the groups Gk’s of typical wave vectors k of the group pig are obtained.

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