Octahedron Calculator

About this calculator

A regular octahedron is one of the five Platonic solids, built from eight equilateral triangular faces, twelve edges and six vertices where four faces meet. Its volume follows V = (√2/3)·a³ and its surface area is 2√3·a², both derived directly from the edge length a since every face and dihedral angle is identical by symmetry; the solid can also be seen as two square pyramids joined base to base.

Crystallographers and mineralogists use octahedral geometry to describe natural crystal habits such as fluorite, spinel, magnetite and diamond, which often grow as octahedra due to their underlying cubic lattice symmetry. Chemists apply the same shape to describe octahedral molecular geometry in coordination complexes, while game designers and 3D modelers use it for eight-sided dice and low-polygon assets.