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Topic: Icosahedral

In the News (Sun 18 Aug 19)

Because the nucleating region is configured correctly for a T=7 icosahedral lattice, the accreting MU's are usually able to locate themselves at the outset with their final nearest neighbors.
Clearly, the icosahedral lattice excels at close-packing MU's, so as an icosahedral lattice is assembled, the sequence of incomplete shells enjoys maximum stability.
For the shell of radius near R=2.28, the distance between neighboring MU's in the final lattice is near one unit, at the minimum of the interaction function.
www.albany.edu /~cmarzec/accrete.sphere.html   (2792 words)

  Geodesic icosahedral golf ball dimple pattern - Patent 5562552
A point is determined in each of the 20 icosahedral triangles of the icosahedron by bisecting the three sides of the icosahedral triangle.
Each geodesic focus point is connected to each apex of the icosahedral triangle so that each geodesic focus point forms a right regular tetrahedron having a base formed by the icosahedral triangle and three triangular faces which merge at the geodesic focus point.
The three base lines 51 form one of the icosahedral triangles, and the line segments 56 which join the midpoints of the sides of the icosahedral triangles form segments of great circles when they are projected onto the spherical surface.
www.freepatentsonline.com /5562552.html   (2829 words)

  Metallurgy of Quasicrystals   (Site not responding. Last check: )
Icosahedral quasicrystal was formed when Fe was substituted by Ru and Os stressing that the stability of icosahedral quasicrystal is dominated by the electronic structure.
This new series of stable icosahedral alloys was shown to possess very sharp peaks comparable to those of a crystalline material and exhibited no detectable peak shifts from the icosahedrally symmetrical positions.
For the Al5.1Li3Cu, the icosahedral phase neighboring crystalline phase is the Al4.8Li3Cu bcc R-phase.
www.nims.go.jp /aperiodic/aperiodic/Team/qcmet.html   (1594 words)

 Spherical Codes with Icosahedral Symmetry
We consider three versions of the problem of placing points on a sphere, subject to the constraint that the points are fixed by the rotations in the icosahedral group of order 60 and determinant 1.
To recover the icosahedral maxvolume arrangements two further files are needed, namely: codes.ivol.txt and ivol.sh.txt, which should be renamed "codes.ivol" and "ivol.sh", respectively.
Fixed points of the icosahedral group are deduced from the number of points in the solution.
www.research.att.com /~njas/icosahedral.codes/index.html   (1106 words)

 Virology Structure
The occurrence of icosahedral features in quite unrelated viruses is not a matter of chance, but a preference.
The simplest icosahedral capsids with 5:3:2 symmetry are built up by using 3 identical subunits to form each triangular face, thereby requiring 60 identical subunits to form a capsid.
In this way it is possible to build a variety of complicated bodies in which 5:3:2 symmetry is preserved and in which the number of subunits is a multiple of 60 as predicted by Crick and Watson.
www.nlv.ch /Virologytutorials/Structure.htm   (960 words)

 Group Left EMBL Heidelberg
The symmetry of the expansion functions is 52 and hence the three fold symmetry elements of icosahedral (or 532) symmetry are not imposed on the reconstruction.
Sixty icosahedrally related planes of data are extracted from each transform so that the presence of the three-fold symmetry in the reconstruction signals agreement between the data from different particles.
The icosahedral sampling of the data forces such a reconstruction to be icosahedral but the eigenvalue spectrum will indicate that it is poorly determined and artifact rich as a result.
www.embl-heidelberg.de /ExternalInfo/fuller/uline.html   (5382 words)

 Water as a network of icosahedral water clusters
It is reasonable that the structure of water should be related to the structures of hexagonal (1h) and cubic (1c) ice that exist at atmospheric pressure.
A connectivity map of the icosahedral structure is shown in Fig.
Although such an icosahedral cluster is capable of tessellation, of its constituent 14-molecule tetrahedra, in three dimensions, albeit increasingly strained with increased size [289] (Fig.5), it is incapable of forming a crystalline structure due to its five-fold symmetry.
www.lsbu.ac.uk /water/clusters.html   (0 words)

 Icosahedral Constructions
The icosahedral symmetry of certain species of radiolaria are well known from the drawings of Ernst Haeckel.
A chiral icosahedral object is featured in his lithograph Gravity, which shows a small stellated dodecahedron perforated in a chiral manner and then populated with colorful creatures.
The icosahedral kaleidoscope, invented by Mobius in 1852, is a set of three mirrors, each a thin circular wedge, with angles of 20.91, 31.72, and 37.37 degrees, respectively.
www.georgehart.com /icosahedral/icosahedral.html   (0 words)

 Chancey, C.C. and O'Brien, M.C.M.: The Jahn-Teller Effect in C60 and Other Icosahedral Complexes.
This work is the first comprehensive theoretical analysis of the Jahn-Teller interaction in C60 and other icosahedral complexes.
The importance of this research derives in part from the increasing, widespread interest in C60 and other molecular clusters and their application in science and industry.
In particular, a chapter is devoted to the connection between the theory and experimental observations, such as ESR (electron spin resonance) effects and molecular spectra.
press.princeton.edu /titles/6243.html   (265 words)

 icotwin butterflies
The images on the left are phase gradient images used to track isotropic and shear components of lattice strain, detectable experimentally in electron microscope images at the picometer level.
Below are some drawings put together for assembling the fringe visibility map of an icosahedral twin.
Below find the visibility band map for icosahedral twins with crystallite thickness in the 5 nm (wide band) to 20 nm (narrow band) range.
newton.umsl.edu /~run/nano/icotwinJMOL.html   (1065 words)

 Icosahedral viruses
The symmetry relations for this construction principle are outlined in the script "Symmetry relationships in icosahedral capsids".
An overview of icosahedral capsid structures with near atomic resolution is found in the web-based databank VIPER (Virus Particle Explorer).
SC Harrison, The familiar and the unexpected in structures of icosahedral viruses, Curr.
www.biologie.uni-hamburg.de /lehre/bza/virus/introicos.htm   (666 words)

 Virus Structure
Icosahedral viruses are very common plant and animal viruses.
The quaternary structure is roughly spherical with icosahedral symmetry.
This is attached by a collar to a contractile tail with helical symmetry.
www.tulane.edu /~dmsander/WWW/224/Structure224.html   (0 words)

 Icosahedral Quasicrystals of Intermetallic Compounds are Icosahedral Twins of Cubic Crystals of Three Kinds, Consisting ...
Icosahedral Quasicrystals of Intermetallic Compounds are Icosahedral Twins of Cubic Crystals of Three Kinds, Consisting of Large (about 5000 Atoms) Icosahedral Complexes in Either a Cubic Body-Centered or a Cubic Face-Centered Arrangement or Smaller (about 1350 Atoms) Icosahedral Complexes in the ß -Tungsten Arrangement
The twofold-axis electron-diffraction photographs of icosahedral quasicrystals are of three kinds, reflecting three different structures of the cubic crystals that by icosahedral twinning form the quasicrystals.
The supporting evidence for these cubic structures is discussed as well as other evidence showing that the simple quasicrystal theory, which states that quasicrystals do not involve any translational identity operations, has to be modified.
www.pnas.org /cgi/content/abstract/86/22/8595   (0 words)

 Adding the Third Dimension to Virus Life Cycles: Three-Dimensional Reconstruction of Icosahedral Viruses from ...
The simplest icosahedral structure is one in which 60 identical subunits interact identically.
A closed icosahedral shell that conforms to the principles of quasi-equivalent symmetry contains 60T subunits organized as hexamer and pentamer units (53).
The positions of the icosahedral twofold (2), fivefold (5), and threefold (3) and the quasi-sixfold (6) axes are indicated.
mmbr.asm.org /cgi/content/full/63/4/862   (9467 words)

 The Icosahedral Server
The closed icosahedral shell, composed of hexamers and pentamers, is generated by inserting 12 pentamers at appropriate positions in the hexamer net.
The icosahedral face for a T=3 surface lattice is defined by the triangle with blue edges (h=1, k=1).
Two possible T=7 lattice choices are also marked with green and yellow lines (h=2, k=1 or h=1, k=2, these being mirror images of each other), and require knowledge of the arrangement of hexamers and pentamers and the enantiomorph of the lattice for a complete lattice definition.
viperdb.scripps.edu /icos_server.php?icspage=paradigm   (372 words)

 Spherical coordinates of icosahedral water clusters
Use of spherical coordinates is nicely applicable to symmetrical systems with molecules positioned on nested concentric spherical surfaces, such as the icosahedral water cluster.
Spherical coordinates of the water oxygen atoms in icosahedral water clusters (ES).
Spherical coordinates of the water oxygen atoms in a super cluster of 13 icosahedral water clusters (ES).
www.btinternet.com /~martin.chaplin/spher.html   (249 words)

 Chord Lengths of a Geodesic Dome
Given these preliminaries, an icosahedral geodesic patch may be created by forming a two-dimensional equilateral mesh and projecting its vertices onto the circumscribed sphere.
The remaining problem is to calculate the lengths of the chords of the icosahedral geodesic patch.
Only one patch needs to be calculated; it is symmetrically repeated to populate the icosahedral geodesic surface; this means we'll be duplicating the edges of the icosahedron when we duplicate the tesselated surfaces, but that's just a bother, not a problem.
www.tekcad.com /monkeyhouse/geodesics/chordlength   (1299 words)

 [No title]
Due to the low dose condition used to minimize the radiation damage to the sample and to preserve the high resolution structure details, large number of images are used to overcome the noises existing in the images and to get high resolution reconstruction.
Classic reconstruction algorithm takes advantage of the icosahedral symmetry (60 fold) usually existing for the spherical virus capsids to greatly enhance the signal to noise ratio; However, there are non-icosahedral components such as viral genome, machinery for packaging/releasing viral genome could not be solved with this icosahedral symmetry averaging.
We are working on new hybrid algorithm that would reconstruct the non-icosahedral components at ~8Å without assuming the high icosahedral symmetry.
acts.nersc.gov /events/Workshop2000/applicants/file_jiang.doc   (398 words)

 Armor-Plated Puzzle - Health - RedOrbit   (Site not responding. Last check: )
Using mathematical arguments and evidence for icosahedral symmetry in X-ray analyses of various viruses, Caspar and Klug proposed that those viruses referred to as spherical viruses- because under microscopes they look like balls-actually have icosahedral symmetry.
In their viral version, the two scientists claimed that they could account for all viruses that have icosahedral symmetry, no matter what their size, using one simple recipe: Place one pentagon at each of the 12 sites of fivefold symmetry and then fill the rest of the shell with hexagonal units.
Indeed, he, Rudnick, and UCLA chemist William M. Gelbart were struck by the fact that experiments dating back to the 1960s showed that viral capsids with icosahedral symmetry will form spontaneously in a solution of capsid proteins, given the right conditions of temperature, pH, and salinity.
www.redorbit.com /news/display?id=236789&source=r_healt   (2310 words)

 Icosahedral Ordering in Liquid and Undercooled Metals — ESRF
distribution of the liquid is found to be very broad and strongly asymmetric towards negative values extending down to the ideal value for a perfect icosahedral cluster.
values very near to the icosahedral limit shows a distinct peak at 60° and a second peak around 110° with a clear minimum at 90°, similar to the ideal case shown by red ticks in the inset.
In conclusion, novel X-ray absorption experimental results on liquid and undercooled liquid copper, interpreted using an advanced data-analysis method based on multiple-scattering simulations are shown to contain direct information on triplet correlations making feasible a reliable determination of the bond-angle distribution and fraction of icosahedral configurations in liquids.
www.esrf.fr /UsersAndScience/Publications/Highlights/2003/XASMS/XASMS03   (809 words)

 Armor-plated puzzle: deciphering the code of viral geometry Science News - Find Articles
What's more, why do the structures of some icosahedral viruses--among them polyoma-type viruses, which are associated with some cancers, and L-A, a yeast virus--fall outside the Caspar-Klug framework.
Using mathematical arguments and evidence for icosahedral symmetry in X-ray analyses of various viruses, Caspar and Klug proposed that those viruses referred to as spherical viruses--because under microscopes look like balls--actually have icosahedral symmetry.
Caspar and Klug were prepared for this leap, in part, by the then-new architectural concept of the geodesic dome conceived by R. Buckminster Fuller.
findarticles.com /p/articles/mi_m1200/is_10_168/ai_n15650954   (835 words)

 Demonstration of the Influence of Local Icosahedral Order on the Nucleation Barrier of Metallic Liquids
To explain this surprising result, F. Frank [1] theorized that as metallic liquids cool, (1) local structures develop in the liquid phase containing icosahedral short-range order (ISRO), which is incompatible with the long-range periodicity of the crystalline phase, and that (2) this incompatibility creates a barrier to the formation of the crystalline phase.
The first event corresponds to the nucleation and rapid growth of a metastable icosahedral quasicrystal; the second event indicates the transformation to the stable C14 crystal phase.
This verifies Frank's hypothesis that the origin of the barrier to nucleation of crystallographic phases is the formation of local icosahedral order in the liquid.
www.aps.anl.gov /Science/Highlights/2003/metallic_liq.htm   (848 words)

 Roughening Transition of Icosahedral Gold Cluster   (Site not responding. Last check: )
A liquid gold sphere with 2624 atoms has been cooled down to 100K to obtain a faceted icosahedral gold cluster.
Although MSD calculation and visual examination shows that surface atoms travel very long distance at 1000K, multi-layer BOP calculations show that the surface structure doesn't change a lot.
This may suggest that surface atoms travel around freely but still keeping the relative positions with neighbor atoms to form the icosahedral structure, which is different from liquid.
www.pas.rochester.edu /~wangyt/research/facet/index.html   (361 words)

 Chancey, C.C. and O'Brien, M.C.M.: The Jahn-Teller Effect in C60 and Other Icosahedral Complexes.
The importance of this research derives in part from the increasing, widespread interest in C60 and other molecular clusters and their application in science and industry.
In particular, a chapter is devoted to the connection between the theory and experimental observations, such as ESR (electron spin resonance) effects and molecular spectra.
Earlier books have discussed the theory of Jahn-Teller interactions in lower symmetry structures (cubic, tetrahedral, tetragonal, trigonal,...); this is the first that focuses on the new icosahedral systems, whose most famous example is Buckminsterfullerene, C60.
pup.princeton.edu /titles/6243.html   (265 words)

 Multidimensional Glossary   (Site not responding. Last check: )
For example, the hexacosichoron and the icosahedral hecatonicosachoron have the same 1200 triangles, but in the former they are shared by 600 tetrahedra and in the latter they are shared by 120 icosahedra.
The vertex figure of the icosahedral hecatonicosachoron is a great dodecahedron of edge 1, whose pentagons are the vertex figures of the twelve icosahedra that meet at each vertex.
The resulting polychoron is called an icosahedral hecatonicosachoron, and it has 120 vertices (the same as the vertices of the preceding star-polychoron), 720 edges (the same as the edges of the preceding star-polychoron), and 1200 triangular faces in addition to its 120 icosahedral cells.
members.aol.com /Polycell/glossary.html   (16070 words)

 The structure of a T = 1 icosahedral empty particle from southern bean mosaic virus -- Erickson et al. 229 (4714): 625 ...
The structure of a T = 1 icosahedral particle (where T is the triangulation number), assembled from southern bean mosaic virus coat protein fragments that lacked the amino-terminal arm, was solved by means of model building procedures with the use of 6-angstrom resolution x-ray diffraction data.
The icosahedral five-, three-, and twofold contacts were found to be similar, at this resolution, to the analogous contacts (icosahedral five-, quasi-three-, and quasi-twofolds) found in the parent T = 3 southern bean mosaic virus.
However, the icosahedral fivefold contacts of the T = 3 structure are the most conserved in the T = 1 capsid.
www.sciencemag.org /cgi/content/abstract/229/4714/625   (0 words)

 Experimental measurement of the photonic properties of icosahedral quasicrystals : Nature
Such quasicrystals can be constructed from two or more types of dielectric material arranged in a quasiperiodic pattern whose rotational symmetry is forbidden for periodic crystals (such as five-fold symmetry in the plane and icosahedral symmetry in three dimensions).
Because quasicrystals have higher point group symmetry than ordinary crystals, their gap centre frequencies are closer and the gaps widths are more uniform—optimal conditions for forming a complete bandgap that is more closely spherically symmetric.
We show that three-dimensional icosahedral quasicrystals exhibit sizeable stop gaps and, despite their quasiperiodicity, yield uncomplicated spectra that allow us to experimentally determine the faces of their effective Brillouin zones.
www.nature.com /doifinder/10.1038/nature03977   (344 words)

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