Recognised as Polyhedron
Octahedron
- Platonic
- 8 faces
- Dual: cube
The octahedron is a Platonic solid with 8 faces, 12 edges and 6 vertices: 8 equilateral triangles. Its dual is the cube, and its dihedral angle is 109.471°.
Faces, edges and vertices
Faces88 equilateral triangles
Edges12
Vertices6
Euler characteristicV − E + F = 6 − 12 + 8 = 2every convex polyhedron gives 2
FamilyPlatonicregular: identical regular faces meeting identically at every vertex
Dual polyhedroncube
Measurements at edge length 1
Volume0.471405cubic units for a unit edge
Surface area3.464102square units for a unit edge
Dihedral angle109.4712°the angle between two adjacent faces
Volume at edge 10471.4045
Surface area at edge 10346.4102
Isoperimetric ratio0.60461 for a sphere; higher means more efficiently packed
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