Octahedron (3D) — free printable diagram

How many faces, edges and vertices an octahedron has

An octahedron is a 3D solid with 8 faces, 12 edges and 6 vertices. Every face is flat, so it is a polyhedron and Euler's formula applies to it.

Solid

Octahedron

Faces

8

Edges

12

Vertices (corners)

6

Volume

V = (√2 ⁄ 3) × a³, where a is the edge length

Surface area

SA = 2√3 × a²

• All 8 faces are the same shape: an equilateral triangle.
• It is one of the five Platonic solids — the only five solids whose faces are all identical regular polygons with the same number of them meeting at every vertex. The complete set is the tetrahedron (4 faces), cube (6), octahedron (8), dodecahedron (12) and icosahedron (20); this is the one with 8.
• It can be read as two square pyramids joined base to base, which is the easiest way to see where the 8 faces and 6 vertices come from.
• Four triangles meet at every vertex. In a cube three squares meet at each of its 8 vertices — the octahedron's 6 vertices and 8 faces are the cube's 8 vertices and 6 faces swapped over, which is what it means to say the two solids are duals.
• Euler's formula holds for every solid with flat faces: faces + vertices − edges = 2. It is the quickest way to check a count you are unsure of. Here that is 8 + 6 − 12 = 2.