Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. A polyhedron with eight plane surfaces.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. a polyhedron with eight faces; the regular octahedron has regular triangles as faces and is one of the Platonic solids.
from the GNU version of the Collaborative International Dictionary of English
 n. A solid bounded by eight faces. The regular octahedron is contained by eight equal equilateral triangles.
from The Century Dictionary and Cyclopedia
 n. A solid bounded by eight faces.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. any polyhedron having eight plane faces
Etymologies
Examples

A pyramid is not a Platonic solid because not all the sides are the same, but by sticking an inverted pyramid on the bottom you get an octahedron, which is.

Each "cigar" has a leaflike body at its base, and in the centre of the octahedron is a globe containing four atoms, each within its own wall; these lie on the dividing lines of the faces, and each holds a pair of the funnels together.
Occult Chemistry Clairvoyant Observations on the Chemical Elements

It is more interesting to me, for instance, to try and find out why the red oxide of copper, usually crystallizing in cubes or octahedrons, makes itself exquisitely, out of its cubes, into this red silk in one particular Cornish mine, than what are the absolutely necessary angles of the octahedron, which is its common form.

Unfortunately, analysis of the finite subgroups of SO (3) isn't so easy, and I don't know any easy way of showing why there should only be the five (or four, actually  symmetries of the cube and the octahedron are the same).

The tetrahedron was fire, the cube earth, the octahedron air, the icosahedron water and the dodecahedron the encompassing dome.

Only five shapes fit the bill: the tetrahedron, the cube, the octahedron, the icosahedron and the dodecahedron, the quintet known as the Platonic solids since Plato wrote about them in the Timaeus.

The octahedron can be made from four cards and an icosahedron with ten of them.

It is possible to closepack the three simple solids — the tetrahedron, octahedron, and cube (all related by the square root of 22) — inside a cube.
Architecture and Memory: The Renaissance Studioli of Federico da Montefeltro

Similarly, an icosahedron may be constructed inside the octahedron, at the concentric heart of the entire ensemble.
Architecture and Memory: The Renaissance Studioli of Federico da Montefeltro

"The cube, rising from a quadrangular base, gives an impression of stability and is therefore identified with the earth; the octahedron, suspended between two opposite points and turned as on a lathe, conveys an image of great mobility, like the air; the icosahedron has the greatest number of sides, and its globular form most closely resembles a drop of water; the tetrahedron's pointed form suggests fire" (PérezGómez, "Glass Architecture," 257).
Architecture and Memory: The Renaissance Studioli of Federico da Montefeltro
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