Definitions
from The American Heritage® Dictionary of the English Language, 5th Edition.
 noun A polyhedron with eight faces.
from The Century Dictionary.
 noun A solid bounded by eight faces.
from the GNU version of the Collaborative International Dictionary of English.
 noun (Geom.) A solid bounded by eight faces. The regular octahedron is contained by eight equal equilateral triangles.
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 noun geometry a
polyhedron witheight faces ; theregular octahedron has regulartriangles as faces and is one of thePlatonic solids .
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 noun any polyhedron having eight plane faces
Etymologies
from The American Heritage® Dictionary of the English Language, 4th Edition
from Wiktionary, Creative Commons Attribution/ShareAlike License
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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.

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.

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).

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.

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

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