On the real combinations of cubes and octahedra

2020 ◽  
Vol 76 (2) ◽  
pp. 206-210
Author(s):  
Yury L. Voytekhovsky ◽  
Dmitry G. Stepenshchikov
Keyword(s):  
Automorphism Group ◽  
Natural Diamond ◽  
Symmetry Point ◽  
The Real ◽  
Diamond Crystals ◽  
Point Groups

All the real combinations of cubes and octahedra (77657 in total) are enumerated and characterized by facet symbols and symmetry point groups. The most symmetrical polyhedra (with automorphism group orders not less than 6, 163 in total) are shown. It is assumed that they represent the most probable forms of natural diamond crystals. The results are discussed with respect to the Curie dissymmetry principle.

Effect of pressure on synthetic diamond crystals at high temperatures and pressures in Fe/Ni catalyst system

CrystEngComm ◽  
2021 ◽  
Author(s):  
Shuai Fang ◽  
Yongkui Wang ◽  
Liangchao Chen ◽  
Zhiyun Lu ◽  
Zhenghao Cai ◽  
...  
Keyword(s):  
Nitrogen Content ◽  
Growth Mechanism ◽  
Synthetic Diamond ◽  
Natural Diamond ◽  
Catalyst System ◽  
Necessary Condition ◽  
Ni Catalyst ◽  
Effect Of Pressure ◽  
Diamond Crystals ◽  
System P

Pressure is a necessary condition for the growth of natural diamond. Studying the effect of pressure on the nitrogen content of diamond is important for exploring the growth mechanism of...

Kleinian characterization of asymptotic symmetries of real general relativity

1993 ◽  
Vol 441 (1913) ◽  
pp. 465-471 ◽  
Keyword(s):  
General Relativity ◽  
Automorphism Group ◽  
Group Action ◽  
Radon Transform ◽  
Symmetry Groups ◽  
Asymptotic Symmetry ◽  
The Real ◽  
The Given ◽  
Asymptotic Symmetries

According to Klein’s Erlanger programme, one may (indirectly) specify a geometry by giving a group action. Conversely, given a group action, one may ask for the corresponding geometry. Recently, I showed that the real asymptotic symmetry groups of general relativity (in any signature) have natural ‘projective’ classical actions on suitable ‘Radon transform’ spaces of affine 3-planes in flat 4-space. In this paper, I give concrete models for these groups and actions. Also, for the ‘atomic’ cases, I give geometric structures for the spaces of affine 3-planes for which the given actions are the automorphism group.

Fullerenes C20-C60: Combinatorial types and symmetry point groups

2002 ◽  
Vol 47 (5) ◽  
pp. 720-722 ◽  
Author(s):  
Yu. L. Voytekhovsky ◽  
D. G. Stepenshchikov
Keyword(s):  
Symmetry Point ◽  
Point Groups

Notiz: Quantification of Symmetry

1996 ◽  
Vol 51 (7) ◽  
pp. 882-883
Author(s):  
Igor Novak
Keyword(s):  
Finite Groups ◽  
Group Element ◽  
Symmetry Point ◽  
Point Groups ◽  
New Criterion

Abstract A new mathematical criterion is suggested for symmetry ranking, i.e. determination of an “absolute symmetry scale” for discrete, finite groups. The criterion is based on both, the periods (orders) of each group element and the order of the group itself. This is different from the current criteria which consider only the orders of the groups themselves. The symmetry ranking, based on the new criterion, is applied to the symmetry point groups.

Contact electrization of natural diamond crystals

2010 ◽  
Vol 36 (2) ◽  
pp. 162-165 ◽  
Author(s):  
E. V. Ryabov ◽  
Yu. S. Mukhachev
Keyword(s):  
Natural Diamond ◽  
Diamond Crystals

Groups of real genus p + 1, where p is prime

2014 ◽  
Vol 14 (03) ◽  
pp. 1550040
Author(s):  
Coy L. May
Keyword(s):  
Finite Group ◽  
Automorphism Group ◽  
Klein Surface ◽  
The Real ◽  
A Finite Group ◽  
Large Groups

Let G be a finite group. The real genusρ(G) is the minimum algebraic genus of any compact bordered Klein surface on which G acts. We classify the large groups of real genus p + 1, that is, the groups such that |G| ≥ 3(g - 1), where the genus action of G is on a bordered surface of genus g = p + 1. The group G must belong to one of four infinite families. In addition, we determine the order of the largest automorphism group of a surface of genus g for all g such that g = p + 1, where p is a prime.

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