A Continuous Symmetry Measure of [4Fe−4S]+Core Distortions and Analysis of Supramolecular Synthons in Crystal Structures of (Et4N)3[Fe4S4Cl4]·Et4NCl at 100 and 295 K

2008 ◽  
Vol 47 (24) ◽  
pp. 11807-11815 ◽  
Author(s):  
Karl S. Hagen ◽  
Mohammad Uddin
Keyword(s):  
Crystal Structures ◽  
Continuous Symmetry ◽  
Supramolecular Synthons ◽  
Symmetry Measure

scholarly journals Morphometric Analysis of Surface Utricles in Halimeda tuna (Bryopsidales, Ulvophyceae) Reveals Variation in Their Size and Symmetry within Individual Segments

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1271
Author(s):  
Jiri Neustupa ◽  
Yvonne Nemcova
Keyword(s):  
Morphometric Analysis ◽  
Outer Surface ◽  
Honeycomb Structure ◽  
Small Scale ◽  
Continuous Symmetry ◽  
Caco3 Content ◽  
Symmetry Measure ◽  
Perfect Symmetry ◽  
Lateral Margins ◽  
The Individual

Calcifying marine green algae of genus Halimeda have siphonous thalli composed of repeated segments. Their outer surface is formed by laterally appressed peripheral utricles which often form a honeycomb structure, typically with varying degrees of asymmetry in the individual polygons. This study is focused on a morphometric analysis of the size and symmetry of these polygons in Mediterranean H. tuna. Asymmetry of surface utricles is studied using a continuous symmetry measure quantifying the deviation of polygons from perfect symmetry. In addition, the segment shapes are also captured by geometric morphometrics and compared to the utricle parameters. The area of surface utricles is proved to be strongly related to their position on segments, where utricles near the segment bases are considerably smaller than those located near the apical and lateral margins. Interestingly, this gradient is most pronounced in relatively large reniform segments. The polygons are most symmetric in the central parts of segments, with asymmetry uniformly increasing towards the segment margins. Mean utricle asymmetry is found to be unrelated to segment shapes. Systematic differences in utricle size across different positions might be related to morphogenetic patterns of segment development, and may also indicate possible small-scale variations in CaCO3 content within segments.

scholarly journals Voronoi Entropy vs. Continuous Measure of Symmetry of the Penrose Tiling: Part I. Analysis of the Voronoi Diagrams

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1659
Author(s):  
Edward Bormashenko ◽  
Irina Legchenkova ◽  
Mark Frenkel ◽  
Nir Shvalb ◽  
Shraga Shoval
Keyword(s):  
Symmetry Group ◽  
Voronoi Diagrams ◽  
Continuous Measure ◽  
Penrose Tiling ◽  
Continuous Symmetry ◽  
Measure Of Symmetry ◽  
Symmetry Measure ◽  
Seed Points

A continuous measure of symmetry and the Voronoi entropy of 2D patterns representing Voronoi diagrams emerging from the Penrose tiling were calculated. A given Penrose tiling gives rise to a diversity of the Voronoi diagrams when the centers, vertices, and the centers of the edges of the Penrose rhombs are taken as the seed points (or nuclei). Voronoi diagrams keep the initial symmetry group of the Penrose tiling. We demonstrate that the continuous symmetry measure and the Voronoi entropy of the studied sets of points, generated by the Penrose tiling, do not necessarily correlate. Voronoi diagrams emerging from the centers of the edges of the Penrose rhombs, considered nuclei, deny the hypothesis that the continuous measure of symmetry and the Voronoi entropy are always correlated. The Voronoi entropy of this kind of tiling built of asymmetric convex quadrangles equals zero, whereas the continuous measure of symmetry of this pattern is high. Voronoi diagrams generate new types of Penrose tiling, which are different from the classical Penrose tessellation.

Continuous Symmetry Measure vs Voronoi Entropy of Droplet Clusters

2021 ◽  
Vol 125 (4) ◽  
pp. 2431-2436
Author(s):  
Mark Frenkel ◽  
Alexander A. Fedorets ◽  
Leonid A. Dombrovsky ◽  
Michael Nosonovsky ◽  
Irina Legchenkova ◽  
...  
Keyword(s):  
Continuous Symmetry ◽  
Symmetry Measure

Three Crystal Structures of Terephthalic Acid Salts of Simple Amines

2009 ◽  
Vol 64 (7) ◽  
pp. 865-870 ◽  
Author(s):  
Peter G. Jones ◽  
Jerzy Ossowski ◽  
Piotr Kus ◽  
Ina Dix
Keyword(s):  
Oxygen Atom ◽  
Crystal Structures ◽  
Terephthalic Acid ◽  
Inversion Symmetry ◽  
Supramolecular Synthons ◽  
Twofold Axis ◽  
Water Oxygen ◽  
Water Oxygen Atom ◽  
Acid Salts

Diphenethylamine forms two adducts (1 : 1, 1a and 2 : 1, 1b) with terephthalic acid (H2TPA). The former is bis(diphenethylammonium)H2TPA・TPA2− and the latter is bis(diphenethylammonium) ・TPA2−. The amine cis-2,6-dimethylpiperidine forms a hydrated 2 : 1 adduct, bis(2,6-dimethylpiperidinium) ・TPA2−・H2O (2). The crystal structures of all three compounds were determined. All H2TPA and TPA2− residues display inversion symmetry, while the water oxygen atom of 2 lies on a twofold axis. Packing analyses have identified some supramolecular synthons known from related structures.

New Aryl Edge - Edge Packing Interactions Involving the N-Oxide Functional Group.

1999 ◽  
Vol 52 (11) ◽  
pp. 1047 ◽  
Author(s):  
Vi T. Nguyen ◽  
Marcia L. Scudder ◽  
A. Noman M. M. Rahman ◽  
Roger Bishop ◽  
Donald C. Craig
Keyword(s):  
Crystal Structures ◽  
Functional Group ◽  
Molecular Assembly ◽  
Potential Importance ◽  
Structural Analogue ◽  
Centrosymmetric Dimer ◽  
Supramolecular Synthons ◽  
Aryl Ring ◽  
X Ray ◽  
Packing Interactions

The X-ray crystal structures of 5b,6,12b,13-tetrahydropentaleno[1,2-b:4,5-b´]diquinoline 5,12-dioxide (5) and (6α,7α,14α,15α)-7,15-dibromo-6,7,14,15-tetrahydro-6,14-methanocycloocta[1,2-b:5,6-b´]diquinoline 5,13- dioxide (6) reveal two new packing modes of potential importance as supramolecular synthons for molecular assembly. Both involve intermolecular edge–edge association of an aryl ring and an N-oxide functionality. One is a bifurcated Ar–H···O(N)···H–Ar interaction which on repetition gives infinite chains of the molecules. The second is a 10-membered centrosymmetric dimer also involving Ar–H···O–N interactions but which merely links two neighbouring molecules of (6). The latter arrangement is a structural analogue of a recently reported dimeric centrosymmetric eight-membered Ar–H···N synthon.

Molecular symmetry and fluorine-containing supramolecular synthons as structure-differentiating agents in some “bridge-flipped” isomeric bis-benzylideneanilines

CrystEngComm ◽  
2014 ◽  
Vol 16 (31) ◽  
pp. 7226-7235 ◽  
Author(s):  
William H. Ojala ◽  
Barjeta Balidemaj ◽  
Jenna A. Johnson ◽  
Sarah N. Larson ◽  
Charles R. Ojala
Keyword(s):  
Crystal Structures ◽  
Molecular Symmetry ◽  
Supramolecular Synthons ◽  
Differentiating Agents

The non-isomorphous crystal structures of “bridge-flipped” isomers1–5are described and are compared to those of recently reported fluorinated benzylideneanilines.

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