Cubic Icosahedra? A Problem in Assigning Symmetry

Lloyd, D. R.

doi:10.1021/ed1002288

Cited by 4 publications

(5 citation statements)

References 19 publications

(26 reference statements)

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“…The major component is consistent with a double-square (2 Â 1) rectangular lattice with unit cell parameters a 1 /2 ¼ a 2 ¼ 27.7 nm and g ¼ 90 . This phase, denoted hereaer as "rectangular," exhibits intense peaks at the simple-square (1 Â 1) positions, but it also displays clear (11), (31), and (51) peaks, which would be forbidden for the…”

Section: X-ray Scatteringmentioning

confidence: 99%

“…[21][22][23][24] Exceptions include TYMV and cowpea mosaic virus (CPMV), for which true 2D crystals with well-dened virus orientation were observed. 19,[25][26][27][28] In particular, electron microscopy (EM) studies [25][26][27] revealed 2D square crystals of TYMV that reected the orthogonality of icosahedral 2-fold axes [29][30][31] (Fig. 1A and B).…”

Section: Introductionmentioning

confidence: 99%

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Crystallization, structural diversity and anisotropy effects in 2D arrays of icosahedral viruses

et al. 2013

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We investigate two-dimensional (2D) assembly of the icosahedral turnip yellow mosaic virus (TYMV) under cationic lipid monolayers at the aqueous solution–vapor interface. The 2D crystallization of TYMV has been achieved by enhancing electrostatically induced interfacial adsorption, an approach recently demonstrated for another virus. In situ X-ray scattering reveals two close-packed 2D crystalline phases of TYMV that are distinct from the previously reported hexagonal and centered square ( 2×2) arrays of TYMV. One of the newly observed phases arises from either a dimeric double-square (2 × 1) or tetrameric square (2 × 2) unit cell. The other is a rhombic crystal with a lattice angle of 80°. The two observed crystal phases are substantially less dense (by over10%) than a 2D lattice of TYMV could be according to its known size and shape, indicating that local anisotropic interparticle interactions play a key role in stabilizing these crystals. TYMV’s anisotropy attributes and numerical analysis of 2D arrays of virus-shaped particles are used to derive a model for the rhombic crystal in which the particle orientation is consistent with the electrostatic lipid–TYMV attraction and the interparticle contacts exhibit steric complementarity. The interplay between particle anisotropy and packing is contrasted between the rhombic crystal model and the square ( 2×2) crystal. This study highlights how the high symmetry and subtle asphericity of icosahedral particles enrich the variety and complexity of ordered 2D structures that can be generated through self-assembly.

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Section: X-ray Scatteringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Crystallization, structural diversity and anisotropy effects in 2D arrays of icosahedral viruses

et al. 2013

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“…An icosahedron is formed by 20 triangular faces and 12 vertices. Given the fact that the cube has 6 faces, by locating a pair of vertices on each cube’s face, the icosahedron might be obtained . Again, to simplify the procedure, we suppose that the cube is centered and aligned along a set of orthogonal axes.…”

Section: Resultsmentioning

confidence: 99%

“…Given the fact that the cube has 6 faces, by locating a pair of vertices on each cube's face, the icosahedron might be obtained. 17 Again, to simplify the procedure, we suppose that the cube is centered and aligned along a set of orthogonal axes. To locate the icosahedron vertices on a cube, it is important to consider the following:…”

Section: Making An Icosahedron From a Cubementioning

confidence: 99%

Platonic Solids and Their Programming: A Geometrical Approach

et al. 2020

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This work covers a three-week program designed to provide undergraduate students with a background in structural chemistry and materials science. Sessions are based on the programming of regular polyhedra and their geometrical relationships by using an object-oriented language (i.e., POV-Ray). Three lectures introduce the basics of programming (syntax), Platonic solids, and the geometrical study of metal clusters and carbon structures. Students work with geometrical aspects of two-dimensional (2D) polygons and generate computer-based algorithms. Next, students study dual three-dimensional (3D) polyhedral shapes, where they adapt the written code to generate Cartesian coordinates of the Platonic solids. Materials to guide the students include an explanation of pseudocodes, tutoring to accompany the programming sessions, reviews of generated codes, and session exercises and challenges. All activities during each hands-on session aim to engage and maintain the initial expectations of the students. Students gain capabilities and knowledge allowing them to code final tests: the C60 molecule; an icosahedral metal cluster; and a cuboctahedron.

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“…Ferritin is given as an example (PDB 1K4R). Icosahedral is not a cubic point group symmetry but has been conflated to the cubic point group symmetry in chemistry [3].…”

mentioning

confidence: 99%

The Assembly of Protein Oligomers — Old Stories and New Perspectives with Graph Theory

Lesieur¹

2014

Oligomerization of Chemical and Biological Compounds

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Cubic Icosahedra? A Problem in Assigning Symmetry

Cited by 4 publications

References 19 publications

Crystallization, structural diversity and anisotropy effects in 2D arrays of icosahedral viruses

Crystallization, structural diversity and anisotropy effects in 2D arrays of icosahedral viruses

Platonic Solids and Their Programming: A Geometrical Approach

The Assembly of Protein Oligomers — Old Stories and New Perspectives with Graph Theory

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