Octahedron in 3D

Two pyramids. One shared square.

A regular octahedron has eight equilateral triangular faces. It can be viewed as two identical square pyramids joined at their bases; the shared square lies inside the solid.

On this page6 sections

faces: 8
edges: 12
vertices: 6

Four triangles meet at every vertex.

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Solid view

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Equal edge a

Units

Units relabel dimensions without conversion.

Opposite vertices

5.657 units

The long diagonal of the regular solid.

Enclosed volume

30.17 units³

√2a³ / 3

Eight triangles of surface

55.426 units²

2√3a²

Open the octahedron along its edges.

The eight equilateral triangles make one connected net. The square equator you see in the solid is an internal cross-section: it does not become an extra face in the net.

Eight equilateral triangles form this octahedron net, with seven folding edges. — Solid outlines mark cut edges; dashed lines mark folds. Face numbers match the model.

8 faces · 12 edges · 6 vertices. Four triangles meet at every vertex. Total surface area = 8 × one triangle = 2√3a².

Eight faces, read as two groups of four.

Octahedron: annotated solid and its component faces — The upper and lower pyramids meet at a square equator. That square is a construction plane, not an extra exterior face.

Octahedron labeled shape diagram in a vertical layout — The upper and lower pyramids meet at a square equator. That square is a construction plane, not an extra exterior face.

A regular octahedron viewed as two square pyramids

The square you cannot count as a face.

Separating the two halves exposes their common equator. In the closed octahedron it is entirely internal. The distance from the equator to either tip is a / √2, so the full tip-to-tip distance is √2a.

2 × ⅓ × a² × a/√2

Two pyramid volumes give the octahedron volume.

Octahedron formulas and current values
Measurement	Formula	Result
Volume	√2a³ / 3	30.17 units³
Surface area	2√3a²	55.426 units²
Center to a vertex	a / √2	2.828 units
Total edge length	12a	48 units

Questions about the shape

Can two arbitrary square pyramids make a regular octahedron?

Only when all twelve outer edges are equal. The pyramid height must be a / √2 for base edge a.

Why does an octahedron have six vertices?

There are four around its equator and one tip above and below it.

Does it have a square face?

The regular octahedron has only triangular exterior faces. The square equator is inside.

Eight triangles.
Six vertices.

Keep the octahedron and its eight-face folding net beside the volume and surface-area formulas.

A regular octahedron in 3D labeled edge a, with 8 triangular faces and 6 vertices. Its eight-triangle net, volume V = √2a³/3 and surface area A = 2√3a² connect the solid to its measurements. — Featured image · Select to enlarge

8 triangular faces: The two square pyramids share an internal equator.
12 equal edges: The label a refers to one outside edge.
V = √2a³ / 3: The volume of the complete regular octahedron.

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