icosahedral group

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icosahedral group

[ī‚käs·ə¦hē·drəl ′grüp]
(mathematics)
The group of motions of three-dimensional space that transform a regular icosahedron into itself.
References in periodicals archive ?
This is the first new class of convex, equilateral polyhedra with icosahedral symmetry in 400 years," says UCLA neuroscientist Stan Schein.
TiCrSi in initial state is characterized by presence of peaks of three phase components: quasi-crystalline [psi]-phase with icosahedral symmetry and lattice spacing [alpha][psi] = 0.
Electron microscopic studies (8,15) have shown particles with a relatively smooth surface capsomeric structure and icosahedral symmetry (Figure 1A).
It had long been known that icosahedral symmetry is not allowed for a periodic object (2).
Quasiperiodic objects can have any of the infinite set of point group symmetries listed as non-crystallographic in the International Tables for Crystallography (4); because they have a single rotation axis of order 5, or one greater than or equal to 7, or have icosahedral symmetry with its six intersecting 5-fold axes.
Over half of all virus families have shells with icosahedral symmetry.
Collectively, this characteristic is called icosahedral symmetry, even when the object isn't 20 sided.
The icosahedral symmetry of the phase was demonstrated by carefully constructing a reciprocal lattice using a series of selected area electron diffraction.
2] with an overall icosahedral symmetry were found in rapidly solidified [Al.
using a computer to select a particular configuration of the 27 copies of p17 within a tile, the team then assembles all tiles according to the rules of icosahedral symmetry.
X-ray scattering experiments demonstrate that these unusual materials appear to have a fivefold icosahedral symmetry, a pattern that fails to fit conventional crystallographic rules.
Penrose also played the three-dimensional version of his tiling game -- packing space with simple blocks, such as pairs of squashed cubes (rhombohedra), that generate nonperiodic solid structures with fivefold or, in three dimensions, icosahedral symmetry.