Regular Octahedron Calculator

The regular octahedron is one of the five Platonic solids. It can be thought of as two square pyramids glued base-to-base, or as the dual of a cube.

Key Properties:

• 8 equilateral triangular faces
• 12 edges (all equal length)
• 6 vertices (each meets 4 faces)
• Dual of the cube (vertices ↔ faces)
• Dihedral angle: arccos(-1/3) ≈ 109.47°

Special Structure:

Place an octahedron inside a cube so that its 6 vertices touch the center of each cube face. The octahedron and cube are dual polyhedra - connecting face centers of one creates the other.