From the Greek, eight-faced or eight-sided, the octahedron is eight equilateral triangles joined along 12 edges to make six vertices or corners. The shape has four pairs of parallel faces.
The Five Solids, also called the Platonic Solids or the Pythagorean Solids, are directly associated as particles of the elements, are seen as the building blocks of reality. By using geometric figures, Pythagoras (and later Plato) implicitly connects the 5 solids to ideas of harmony and symmetry, and as such offer insights into the nature of the cosmos.
The octahedron symbolizes Air, according the Plato and the other Pythagoreans.