The colour-symmetry groups and cryptosymmetry groups associated with the 32 crystallographic point groups

1962 ◽  
Vol 117 (1-6) ◽  
Author(s):  
OSCAR WITTKE
Keyword(s):  
Symmetry Groups ◽  
Point Groups

3D Braided Geometry Structures Based on Space Group

2010 ◽  
Vol 152-153 ◽  
pp. 1156-1161 ◽  
Author(s):  
Wen Suo Ma ◽  
Bin Qian Yang ◽  
Xiao Zhong Ren
Keyword(s):  
Group Theory ◽  
Symmetry Groups ◽  
The Novel ◽  
Geometrical Structures ◽  
Braided Group ◽  
Space Group ◽  
Space Groups ◽  
Geometry Structure ◽  
Point Groups ◽  
Space Point

3D braided group theory is dissertated. The analysis procedure is described from the existing braided geometry structure to the braided space group; 3D braided geometrical structures are finally described by means of group theory. Some of novel 3D braided structures are deduced from the braided space groups. By describing the 3D braided materials with braided space point and braided space groups, the braided space groups are not always the same as symmetry groups of crystallographic because novel lattices can be produced and the reflection operation cannot exist in braided space point groups. Braided point and space groups are theoretical basis for deriving the novel braided geometry structure.

Ferroelectric space groups

1986 ◽  
Vol 42 (1) ◽  
pp. 44-47 ◽  
Author(s):  
D. B. Litvin
Keyword(s):  
Electric Dipole ◽  
Space Time ◽  
Discrete Space ◽  
Symmetry Groups ◽  
Space Groups ◽  
Point Groups

The 440 ferroelectric space groups, viz the Heesch-Shubnikov (magnetic) space groups, which are symmetry groups of ferroelectric electric-dipole arrangements in crystals, are derived and tabulated. By considering automorphisms induced by the automorphisms of the discrete space-time group, we show that although ferroelectric, ferromagnetic and ferrocurrent point groups all number 31, the number of ferroelectric space groups differs from 275, which is that of both ferromagnetic and ferrocurrent space groups.

SINIF CEBİRİ YAKLAŞIMI ALTINDA 𝑫𝟐𝒅 ve 𝑪𝟑𝒊 NOKTA GRUPLARI

2021 ◽  
Vol 8 (17) ◽  
pp. 141-149
Author(s):  
Melike DEDE ◽  
Harun AKKUS
Keyword(s):  
Symmetry Groups ◽  
Character Tables ◽  
Secular Equations ◽  
Point Groups ◽  
Cayley Tables

In this study, the point groups 𝐷2𝑑 and 𝐶3𝑖 which belong to tetragonal and trigonal crystal systems, respectively, are handled under the class sum approach. Symmetry groups were formed with symmetry elements that left these point groups unchanged and Cayley tables of related groups were obtained. Using these tables, the conjugates of the elements and the classes of the group were formed. Secular equations are written for each class sum obtained by the sum of the elements that make up the class. By solving these secular equations, the character vectors are obtained. Thus, the character tables were reconstructed with the calculated characters for both point groups under the class sum approach.

MULTIPLE-Q STRUCTURES IN FRUSTRATED ANTIFERROMAGNETS

1993 ◽  
Vol 07 (16n17) ◽  
pp. 2981-3002 ◽  
Author(s):  
M.W. LONG
Keyword(s):  
Phase Transitions ◽  
Theoretical Research ◽  
Symmetry Groups ◽  
Frustrated Magnets ◽  
Spin States ◽  
Magnetic Structures ◽  
Point Groups ◽  
Magnetic States ◽  
Physical Phenomena

The concepts relevant to frustrated antiferromagnets are briefly reviewed. Antiferromagnets are classified according to their symmetry groups, with non-trivial point groups leading to the possibility of multiple-Q antiferromagnetism. The role of residual degeneracy is highlighted and the manner in which this degeneracy is lifted is discussed. The physical phenomena in competition within frustrated magnets, and the states that they prefer, yield ongoing theoretical research, and the way neutron scattering can be used, in conjunction with the application of pressure and magnetic fields, to determine which of the possible magnetic structures is stabilised is under experimental scrutiny. Multiple-Q antiferromagnetism finds varied and often exotic spin states with similar energies, and as such is the setting in which phase transitions between different magnetic states can be studied.

Molecular Rovibronic Symmetries in Electric and Magnetic Fields

1975 ◽  
Vol 53 (19) ◽  
pp. 2210-2220 ◽  
Author(s):  
James K. G. Watson
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Electric Field ◽  
Symmetry Groups ◽  
Nuclear Spins ◽  
Symmetry Classification ◽  
Electric And Magnetic Fields ◽  
Field Symmetry ◽  
Point Groups

The structures of the symmetry groups for the rovibronic levels of a molecule in a homogeneous electric or magnetic field are derived, and the symmetry classification of the levels in terms of the representations and corepresentations of these groups is discussed. Specific results are given for molecules of the point groups C3, C2v, C3v, D2d, and Td in an electric field. Symmetry in combined electric and magnetic fields and the inclusion of nuclear spins are considered briefly.

scholarly journals CARTESIAN AXIS AND PLANE CONVENTIONS IN Cnv SYMMETRY GROUPS

Química Nova ◽  
2021 ◽  
Author(s):  
Lucas Dias ◽  
Roberto Faria
Keyword(s):  
Water Molecule ◽  
Point Group ◽  
Molecular Orbitals ◽  
Symmetry Groups ◽  
Long Time ◽  
Point Groups

In this work, we call the attention to the ambiguity found in the literature when labeling vibrations and molecular orbitals as B1 and B2 for molecules belonging to the C2v point group as, for example, the water molecule. A survey of several books and some articles shows that this ambiguity comes from a long time ago and persists today, being a source of misunderstanding and a waste of time for students and teachers. It means that, in the case of the point groups Cnv, Dn, and Dnh (n = 2, 4, 6), it is very important to draw students’ attention to this ambiguity that exists in the literature. It is unfortunate that the recommendation made by Mulliken, more than sixty years ago, to always place the water molecule in the yz plane, has not been followed.

scholarly journals Fundamental Domains for Rhombic Lattices with Dihedral Symmetry of Order 8

10.37236/7802 ◽  
2019 ◽  
Vol 26 (3) ◽  
Author(s):  
Joseph Ray Clarence G. Damasco ◽  
Dirk Frettlöh ◽  
Manuel Joseph C. Loquias
Keyword(s):  
Symmetry Group ◽  
Fundamental Domain ◽  
Point Group ◽  
Symmetry Groups ◽  
Fundamental Domains ◽  
Open Case ◽  
Point Groups ◽  
Index 2 ◽  
Rhombic Lattice ◽  
Planar Lattices

We show by construction that every rhombic lattice $\Gamma$ in $\mathbb{R}^{2}$ has a fundamental domain whose symmetry group contains the point group of $\Gamma$ as a subgroup of index $2$. This solves the last open case of a question raised in a preprint by the authors on fundamental domains for planar lattices whose symmetry groups properly contain the point groups of the lattices.  

The symmetry groups of the regular tessellations of S 2 and S 3

1982 ◽  
Vol 383 (1785) ◽  
pp. 379-398 ◽  
Keyword(s):  
Irreducible Representations ◽  
Symmetry Groups ◽  
Character Tables ◽  
Point Groups

The construction of the symmetry groups is described for the regular complexes that tessellate S 2 and S 3 . For S 3 these groups are four-dimensional point groups, and they are described in this paper both in terms of their presentations and as subgroups of products of the binary polyhedral groups. The second description is used to obtain the irreducible representations of the symmetry groups; the character tables are also given.

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