Eight triangular faces, twelve edges, six vertices. The cleanest way to picture it: two square pyramids glued base to base — a 'diamond' shape.
Spin the solid
Octahedron
faces
8
8
edges
12
12
vertices
6
6
V − E + F = 6 − 12 + 8 = 2
drag to rotate
Octahedron facts
- 8 faces (equilateral triangles), 12 edges, 6 vertices — Euler: 8 − 12 + 6 = 2.
- 4 faces meet at every vertex.
- It's the dual of the cube — put a vertex at the centre of each of the cube's 6 faces and connect them up.
- Slice it through the middle and the cross-section is a perfect square; natural fluorite and diamond crystals often grow as octahedra.
Volume from the edge length
≈ 0.471 a³.
Your turn
An octahedron has 8 faces and 6 vertices. Use Euler's formula V − E + F = 2 to find its number of edges.