Platonic Solids · 3D

Octahedron

{3,4} · Air

Eight triangles: two square pyramids base to base. Spun between finger and thumb it seems weightless, as Plato’s air.

Turn it in your hands, strike it to hear the chord of its edges, slice it with a plane or lift it into four dimensions.

Facts

Its shadow down a face axis is a hexagram inside a hexagon.
Its dual is the cube; together they form a compound whose edges cross at right angles.
It is the middle phase of Fuller’s Jitterbug.
Many crystals grow as octahedra: fluorite, magnetite, diamond.