Octahedron Calculator

Octahedron Volume and Surface Area Calculator

Calculate the volume and surface area of a regular octahedron. Essential for crystallography, geometric modeling, and mathematical applications.

An octahedron is a three-dimensional geometric shape with eight equilateral triangular faces. This calculator helps you determine its volume and surface area based on the edge length.

Formula

Volume = √2a³/3
Surface Area = 2a²√3

Where:

  • a:length of any edge of the octahedron

Understanding the Octahedron

The octahedron is one of the five Platonic solids, featuring 8 equilateral triangular faces, 12 edges, and 6 vertices. Each vertex is the meeting point of four faces.

Applications

Octahedra appear in crystal structures, particularly in diamond cubic crystal systems. They're also used in gaming as eight-sided dice (d8) and in architectural design.

Frequently Asked Questions

What makes an octahedron regular?

A regular octahedron has faces that are all congruent equilateral triangles, with the same number of faces meeting at each vertex.

How is an octahedron related to a cube?

An octahedron is the dual polyhedron of a cube. The vertices of an octahedron correspond to the face centers of a cube, and vice versa.