octahedron

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polyhedron

polyhedron (pŏlˌēhēˈdrən), closed solid bounded by plane faces; each face of a polyhedron is a polygon. A cube is a polyhedron bounded by six polygons (in this case squares) meeting at right angles. Although regular polygons are possible for any number of sides, there are only five possible regular polyhedrons, having congruent faces, each a regular polygon and meeting at equal angles. The five regular polyhedrons are also known as the Platonic solids, although they were known to the Greeks before the time of Plato. They are the tetrahedron, bounded by four equilateral triangles; the hexahedron, or cube, bounded by six squares; the octahedron, bounded by eight equilateral triangles; the dodecahedron, bounded by twelve regular pentagons; and the icosahedron, bounded by twenty equilateral triangles. The 18th-century Swiss mathematician Leonhard Euler showed that for any simple polyhedron, i.e., a polyhedron containing no holes, the sum of the number of vertices V and the number of faces F is equal to the number of edges E plus 2, or V+F=E+2.

octahedron

[‚ak·tə′hē·drən]
(mathematics)
A polyhedron having eight faces, each of which is an equilateral triangle.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

octahedron

a solid figure having eight plane faces
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
References in periodicals archive ?
The Raman band around 780-830 [cm.sup.-1] is corresponding to the vibrational modes of a regular Nb[O.sub.4] tetrahedron, and the band near 500-700 [cm.sup.-1] is assigned as the symmetric stretching mode of the Nb[O.sub.6] octahedra [1, 18, 19].
On the relationship between the MOFs with different topology s, MIL-53(Al) with one rhombic-shaped pores has two kinds of adsorption sites, ethane and propane are preferential adsorbed at the energetic effect site which is near the AlO4(OH)2 octahedra due to the strong vander hoff interactions between the framework and the longer alkanes, while methane with smaller size prefers to occupy the less energetical adsorption site arising from the space hindrance effect in the main channel.
Changes in surface area increase and the pore size distribution were dependent on the structure and leaching ability of cations from the interlayer and octahedra. Dehydration of mixed-layer vermiculites were observed at the two endothermic effects.
In this way both face surfaces could be the same with alternating regions of silica tetrahedral and alumina octahedra.
1991), and the octahedra most likely pyrite, based on their distinctive morphology and elemental composition.
Here the alumina octahedra replace all but two of their hydroxyl groups by sharing oxygen atoms with the silica sheets.
We soon learned that microscopic crystals of dry ice had already been observed as cubes, octahedra, and cuboctahedra, so we felt ourselves on reasonably safe ground and proceeded with our quest.
This structure contains layers of a single P atom surrounded by six Cr[Se.sub.6] octahedra in the ab plane, as pictured in Figure 2.
The thermodynamically stable form consists of 2 similar chains of Mo[O.sub.6] octahedra aligned in ab configuration [22].
Thus the factors like Nb-O stretching, O-Nb-O bending, Ca-O stretching, and the vibrations involving chain bonds and the broadening of the peaks indicate a slightly distorted (Nb[O.sub.6] octahedra) crystal structure.
[alpha]-[Al.sub.2] 14.16 Corundum--distorted [O.sub.3] octahedra. Al-catechin complex 13.85 Al-complex with irregularly arranged phenolic molecules.
In dimension four, mathematicians have long had a prime candidate for the best kissing arrangement: the 24-cell, a perfectly symmetric shape with 24 comers and 24 three-dimensional sides that are all regular octahedra. If one four-dimensional sphere is placed at each corner, these 24 spheres all kiss the central sphere.

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