# octahedron

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Related to octahedrons: regular octahedron

## 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 ?
Splitting the 3[d.sup.3] electron energy level in the octahedron can lead to an energy-level transition, which is directly associated with mineral colors [25].
One thing that really worked well with % my students was an octahedron that I developed to be the format for them to investigate the Principles of Design.
Thus, the cube has 8 vertices, an octahedron has 6, icosahedron has 12, a dodecahedron has 20, for a total of 46, which accounts for the first 92 elements or half of the Periodic Chart.
The paper gives a detailed analysis of several space-filling polyhedrons deployment, namely, cube deployment, hexagonal prism deployment, rhombic dodecahedron deployment, and truncated octahedron deployment as shown in Figure 4.
Analogical geometrical relations can also be found creating a dynamic model of cubes and regular octahedrons duality (Fig.
It was shown that a limited variation of octahedrons or flat ellipsoids can provide optimized solutions, offering more realistic S/V-relationships as in the case of spheres, which is crucial for cement hydration (Bullard and Garboczi, 2006).
The very high prices which collectors have always been willing to pay for Alpine pink fluorite specimens have inspired unscrupulous sellers to glue fluorite crystals (or even cleavage octahedrons) where they don't belong on matrix rock or on the faces of quartz crystals.
Joyce, "A 1.7-kilobase single-stranded DNA that folds into a nanoscale octahedron" (2004) 427 Nature 618; Hao Yan et al., "DNA-templated self-assembly of protein arrays and highly conductive nanowires" Science 301 (26 September 2003) 1882.
In a feat of molecular engineering, scientists recently designed a strand of DNA that can spontaneously fold into an octahedron.
As is well known, triclinic ZnMo[O.sub.4] is composed of a series of distorted Mo-O tetrahedrons, Zn-O pentahedrons, and ZnO octahedrons. In a distorted Mo-O tetrahedron, the Mo atom is surrounded by four oxygen atoms.
The local coordination geometry of the two sodium centers[NaO6] could be best depicted as slightly distorted octahedrons. The aromantic p-p stacking plays a considerable part in the constitution of 3D network.
Using the NMR and Mossbauer spectroscopy it was found that dissolution velocities of [Al.sup.3+] and [Fe.sup.3+] from octahedrons and tetrahedrons of smectites are similar but with increasing replacement of Al for Mg and/or Fe the dissolution velocity from octahedrons increases (Novak and Cicel, 1978).

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