Search results
Results From The WOW.Com Content Network
A cube has the same set of symmetries, since it is the polyhedron that is dual to an octahedron. The group of orientation-preserving symmetries is S 4 , the symmetric group or the group of permutations of four objects, since there is exactly one such symmetry for each permutation of the four diagonals of the cube.
Structural distortion analysis Determination of regular and irregular distorted octahedral molecular geometry; Octahedral distortion parameters [5] [6] [7] Volume of the octahedron; Tilting distortion parameter for perovskite complex [8] Molecular graphics. 3D modelling of complex; Display of the eight faces of octahedron
The Jahn–Teller effect (JT effect or JTE) is an important mechanism of spontaneous symmetry breaking in molecular and solid-state systems which has far-reaching consequences in different fields, and is responsible for a variety of phenomena in spectroscopy, stereochemistry, crystal chemistry, molecular and solid-state physics, and materials science.
For a free ion, e.g. gaseous Ni 2+ or Mo 0, the energy of the d-orbitals are equal in energy; that is, they are "degenerate". In an octahedral complex, this degeneracy is lifted. The energy of the d z 2 and d x 2 −y 2, the so-called e g set, which are aimed directly at the ligands are destabilized.
The ideal tetrahedron, cube, octahedron, and dodecahedron form respectively the order-6 tetrahedral honeycomb, order-6 cubic honeycomb, order-4 octahedral honeycomb, and order-6 dodecahedral honeycomb; here the order refers to the number of cells meeting at each edge. However, the ideal icosahedron does not tile space in the same way.
A regular octahedron is an octahedron that is a regular polyhedron. All the faces of a regular octahedron are equilateral triangles of the same size, and exactly four triangles meet at each vertex. A regular octahedron is convex, meaning that for any two points within it, the line segment connecting them lies entirely within it.
In their early 1957 paper on what is now called pseudo Jahn–Teller effect (PJTE), Öpik and Pryce [2] showed that a small splitting of the degenerate electronic term does not necessarily remove the instability and distortion of a polyatomic system induced by the Jahn–Teller effect (JTE), provided that the splitting is sufficiently small (the two split states remain "pseudo degenerate ...
The deltoidal icositetrahedron is a member of a family of duals to the uniform polyhedra related to the cube and regular octahedron. When projected onto a sphere (see right), it can be seen that the edges make up the edges of a cube and regular octahedron arranged in their dual positions. It can also be seen that the 3- and 4-fold corners can ...