Mystical systems
Octahedron
Direct answer
Octahedron: The octahedron is the Platonic solid with eight equilateral triangles for faces, four meeting at each of its six corners, and twelve edges. Plato assigned it to air.
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At a glance
- Also called
- eight faced solid
- Found in
- Mystical Systems
- Related
- Platonic Solids, Timaeus, Tetrahedron, Icosahedron
The octahedron is the Platonic solid with eight equilateral triangles for faces, four meeting at each of its six corners, and twelve edges. Plato assigned it to air.
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What is an octahedron?
A regular octahedron looks like two square-based pyramids set base to base. It is the partner of the cube: put a point at the centre of each of the cube's six faces, join them, and an octahedron results, and the same step applied to the octahedron gives back a cube.
Plato gives it to air in the Timaeus, as a body midway in sharpness and mobility between the tetrahedron of fire and the icosahedron of water. Because all three are built of the same triangles, he lets them change into one another by regrouping their faces: the twenty triangles of one particle of water, he says, can come apart into two of air and one of fire. It is an early attempt to explain change by rearranging parts.
On the tree of the hidden arts: Sacred geometry.
What sets Octahedron apart
The octahedron is the solid of the three axes. Its six corners lie one each way along the lines of height, breadth and depth, so it is the shape marked out by the ends of three equal rods crossed at right angles. Sliced through its middle it shows a square, and at another tilt a regular hexagon. In Plato's physics it is the go-between, the body into which water breaks down and from which fire is made.
- Faces, corners, edges: eight, six and twelve
- Face shape: equilateral triangle, four meeting at each corner
- Dual: the cube
- Plato's element: air, in the Timaeus
- Plato's sum: one particle of water, twenty faces, yields two of air and one of fire
- In minerals: the cleavage form of fluorite and a common form of rough diamond
Often mistaken for something else: The cube has six square faces and eight corners; the octahedron has eight triangular faces and six corners. Each fits inside the other.
The story behind Octahedron
The solid is described in the Timaeus, about 360 BCE, and constructed in the thirteenth book of Euclid's Elements. Ancient writers credit Theaetetus, a friend of Plato, with the first full study of it. Nature makes the shape without help: crystals of fluorite split into octahedra, and many rough diamonds are found in that form, which mineralogists of the eighteenth and nineteenth centuries explained by the regular stacking of their smallest parts.
Why Octahedron matters
Octahedron’s pairing with the cube is the plainest case of duality among the solids, a real pattern that needs no symbolism to be striking.
How to read Octahedron
Geometers use it for the dual of the cube; mineralogists for a crystal habit; sacred geometry as the body of air, often linked with breath.
Octahedron in practice: an example
A reader holding an eight-sided die from a board game is holding a regular octahedron, and can check that four triangles meet at every point.
Where readings of Octahedron go wrong
Crystals grow as octahedra for reasons of atomic packing, and the shape gives a stone no special property.
Sources and editorial method
This entry summarizes the tradition in the Almanac's own words; where no source is listed, it is an editorial summary rather than a primary text, and symbolic readings are named as the tradition's, not as fact.
- Source
- The Great Almanac Dictionary
- Category
- Mystical Systems
- Aliases
- octahedron meaning, octahedron sacred geometry, octahedron air element, regular octahedron, eight faced solid
- Last updated
- 2026-09-26
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Common questions
What is an octahedron?
It is a solid with eight faces. The regular octahedron, one of the five Platonic solids, has eight equilateral triangles, six corners and twelve edges, and can be seen as two square pyramids joined at their bases.
Which element is the octahedron?
Plato's Timaeus assigns it to air. He ranks it between the tetrahedron of fire and the icosahedron of water, since it has more faces than the one and fewer than the other.
How are the cube and the octahedron related?
They are duals. The cube has six faces and eight corners, the octahedron eight faces and six corners, and both have twelve edges. The face centres of either one are the corners of the other.
