Introduction to papers on crystals with fivefold symmetry

1986 ◽  
Vol 20 (9) ◽  
pp. 1185-1186
Author(s):  
Dan Schectman
Keyword(s):  
Fivefold Symmetry

Observation of fivefold symmetry structures in computer models of dense packing of hard spheres

2007 ◽  
Vol 353 (32-40) ◽  
pp. 3545-3549 ◽  
Author(s):  
A.V. Anikeenko ◽  
N.N. Medvedev ◽  
A. Bezrukov ◽  
D. Stoyan
Keyword(s):  
Hard Spheres ◽  
Computer Models ◽  
Dense Packing ◽  
Fivefold Symmetry

Ontogeny in the fossil record: diversification of body plans and the evolution of “aberrant” symmetry in Paleozoic echinoderms

Paleobiology ◽  
2007 ◽  
Vol 33 (1) ◽  
pp. 149-163 ◽  
Author(s):  
Colin D. Sumrall ◽  
Gregory A. Wray
Keyword(s):  
Great Reduction ◽  
Fossil Record ◽  
Evolutionary History ◽  
Total Loss ◽  
Cambrian Explosion ◽  
Growth Stages ◽  
Ecological Constraints ◽  
Fivefold Symmetry ◽  
Primary Body ◽  
History Of

Echinoderms have long been characterized by the presence of ambulacra that exhibit pentaradiate symmetry and define five primary body axes. In reality, truly pentaradial ambulacral symmetry is a condition derived only once in the evolutionary history of echinoderms and is restricted to eleutherozoans, the clade that contains most living echinoderm species. In contrast, early echinoderms have a bilaterally symmetrical 2-1-2 arrangement, with three ambulacra radiating from the mouth. Branching of the two side ambulacra during ontogeny produces the five adult rays. During the Cambrian Explosion and Ordovician Radiation, some 30 clades of echinoderms evolved, many of which have aberrant ambulacral systems with one to four rays. Unfortunately, no underlying model has emerged that explains ambulacral homologies among disparate forms. Here we show that most Paleozoic echinoderms are characterized by uniquely identifiable ambulacra that develop in three distinct postlarval stages. Nearly all “aberrant” echinoderm morphologies can be explained by the paedomorphic ambulacra reduction (PAR) model through the loss of some combination of these growth stages during ontogeny. Superficially similar patterns of ambulacral reduction in distantly related clades have resulted from the parallel loss of homologous ambulacra during ontogeny. Pseudo-fivefold symmetry seen in Blastoidea and the true fivefold symmetry seen in Eleutherozoa result from great reduction and total loss, respectively, of the 2–1–2 symmetry early in ontogeny. These ambulacral variations suggest that both developmental and ecological constraints affect the evolution of novel echinoderm body plans.

Fivefold symmetry as an inhibitor to hard-sphere crystallization

2011 ◽  
Vol 83 (6) ◽  
Author(s):  
Nikos Ch. Karayiannis ◽  
Rohit Malshe ◽  
Juan J. de Pablo ◽  
Manuel Laso
Keyword(s):  
Hard Sphere ◽  
Fivefold Symmetry

PLANAR PATTERNS WITH FIVEFOLD SYMMETRY AS SECTIONS OF PERIODIC STRUCTURES IN 4-SPACE

1990 ◽  
Vol 04 (15n16) ◽  
pp. 2217-2268 ◽  
Author(s):  
M. BAAKE ◽  
P. KRAMER ◽  
M. SCHLOTTMANN ◽  
D. ZEIDLER
Keyword(s):  
Detailed Analysis ◽  
Periodic Structures ◽  
Root Lattice ◽  
Fivefold Symmetry ◽  
Dual Complex

Two quasiperiodic planar patterns with fivefold symmetry are derived from the root lattice A4 in 4-space. A detailed analysis of the geometry of the A4 Voronoi complex and its dual complex is presented with special emphasis on fivefold symmetry. By means of the general dualization method, 2D patterns are obtained, one with triangular tiles and a second which turns out to be the well-known Penrose pattern. The vertex configurations and their relative frequencies, the deflation rules, and the Fourier properties of these patterns are worked out in the framework of the dualization method and Klotz construction.

Fivefold Symmetry in Superlattices of Monolayer-Protected Gold Nanoparticles

2006 ◽  
Vol 110 (29) ◽  
pp. 14040-14045 ◽  
Author(s):  
Hiroshi Yao ◽  
Takayuki Minami ◽  
Akihiko Hori ◽  
Masaya Koma ◽  
Keisaku Kimura
Keyword(s):  
Gold Nanoparticles ◽  
Fivefold Symmetry

The search for liquid fivefold symmetry

Physics World ◽  
2001 ◽  
Vol 14 (3) ◽  
pp. 20-21 ◽  
Author(s):  
Elaine DiMasi
Keyword(s):  
Fivefold Symmetry

scholarly journals The role of fivefold symmetry in suppressing crystallization

2016 ◽  
Vol 7 (1) ◽  
Author(s):  
Jade Taffs ◽  
C. Patrick Royall
Keyword(s):  
Fivefold Symmetry

Gold Microcrystals of Pentagonal Symmetry

1967 ◽  
Vol 25 ◽  
pp. 342-343
Author(s):  
W. R. Bottoms ◽  
R. H. Morriss
Keyword(s):  
Chemical Reduction ◽  
Colloidal Suspensions ◽  
Face Centered Cubic ◽  
Gold Particles ◽  
Fivefold Symmetry ◽  
Impurity Atoms ◽  
Face Centered ◽  
Pentagonal Symmetry ◽  
Pentagonal Crystal ◽  
Gold Microcrystals

Face-centered cubic metallic crystals exhibiting fivefold symmetry have been observed by a number of investigators. Schwoebel has recently observed this anomalous structure in carbon replicas of gold which was vapor deposited onto electropolished gold single crystals. His results are consistent with a model proposed by Melmed and Hayward according to which the pentagonal crystal consists of five segments, each separated by a twin boundary. In an effort to explain this unusual morphology, Schwoebel has suggested the possibility of impurity atoms with a diameter approximately 0.7 that of gold serving as nuclei around which five gold atoms cluster in a modified close-packed arrangement.In this study microcrystals of gold exhibiting a similar structure have been observed in colloidal suspensions prepared by the chemical reduction of chlorauric acid with oxalic acid. The hydrosols contain gold particles of three general morphologies: thin platelets of trigonal symmetry, cube-octahedra with the {111} faces primarily developed and the {100} faces developed to a lesser extent, and particles exhibiting fivefold symmetry.

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