# octahedron

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Related to octahedron: tetrahedron

## 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 ?
Such was the quality--and in many instances the sheer fame--of these great old specimens that one had the impulse to fall to one's knees; for here was the great, famous specimen with two crossed emerald crystals from Hiddenite, North Carolina; an unbelievably fine and beautiful Michigan copper/calcite; a complete octahedron of franklinite fully 12 cm on edge, in matrix, from Franklin, New Jersey; a marvelous Bristol, Connecticut chalcocite; and finally the "Roebling" fluorapatite from the Pulsifer quarry, Maine--surely one of the top, say, ten mineral specimens of any kind in the world.
Bancroft (1984) tantalizingly points out that the overall shape of the "Cullinan" indicates that it was actually the smaller half of an enormous, cleaved octahedron, and somewhere the still-buried larger half of the same crystal must certainly still exist.
The aim of the experiment is to study the position of Mg replacing Al in the Mt octahedron and interaction with interlayer [Na.sup.+] in detail.
Caption: Figure 4: Surface morphology of SrTi[O.sub.3] after being subjected to hot corrosion in [Na.sub.2]S[O.sub.4] + 50 wt.% [V.sub.2][O.sub.5] environment at 900[degrees]C, (a and b) lower and higher magnification images of SrTi[O.sub.3], shows octahedron shaped morphology.
The center of the octahedron is being occupied by [Al.sup.3+], [Mg.sup.2+], and [Fe.sup.2+], sometimes by [Fe.sup.3+] and Li+, amongst others.
The vibration modes at 260 (256), 276, and 322 (323) [cm.sup.-1] are related to Li[O.sub.6] octahedron, the diffusion of Li-O bonds, the O-Nb-O bond, and the diffusion of Li-O atoms at surface during RHT.
And N3 atom from the phenanthroline ligand and O1, N1, and O3 atoms from the Schiff base ligand are located in the equatorial plane of the octahedron. The Schiff base ligand coordinates to Ni1 atom to form one five-membered ring and one six-membered ring, thus increasing the stability of the complex.
Above trends could be obtained from the results of samples A and B, supporting the catalytic property of M[O.sub.4] tetrahedron is superior to that of M[O.sub.6] octahedron. Due to more defects in sample C, its photocatalytic activity decreases in comparison with sample B.
For example, some researchers believe that pink originated from the absorption of d-d transition ofMn in the octahedron, while others hypothesize it is the result of a color heart, similar to smoky quartz [9].
Out of the ordinary as they may appear, you have probably seen them before: a visor crown covering Beyonc`'s head as she meditated and spun in her music video for 7/11; a stellated octahedron propped atop one of Erykah Badu's iconic tall hats as the singer performed in Philadelphia and New York last week; and a bone-white halo on the cover for 'Awaken, My Love!', the most recent album from Childish Gambino, also known as Donald Glover.
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.
These tetrahedrons have common atoms of selenium on the tops of the octahedron [1-3].

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