How to Calculate Octahedron
What is Octahedron?
A regular octahedron is one of the five Platonic solids, with 8 equilateral triangular faces, 12 edges, and 6 vertices. It looks like two square pyramids joined at the base.
Formula
V = (√2/3)a³; SA = 2√3 a²
- a
- edge length (length)
- V
- volume (length³)
- SA
- surface area (length²)
Step-by-Step Guide
- 1Volume = (√2/3) × a³
- 2Surface area = 2√3 × a²
- 3Face diagonal = a√2
- 4Height = a√2
Worked Examples
Input
Edge a = 4
Result
Volume ≈ 30.17, SA ≈ 55.42
Input
Edge a = 6
Result
Volume ≈ 101.82, SA ≈ 124.71
Frequently Asked Questions
Why is the octahedron called a Platonic solid?
It's one of five Platonic solids: all faces are congruent regular polygons, and the same number of faces meet at each vertex.
How many vertices, edges, and faces does an octahedron have?
The octahedron has 6 vertices, 12 edges, and 8 equilateral triangular faces.
What is the dual polyhedron of an octahedron?
The cube (hexahedron) is the dual. Its vertices correspond to the octahedron's face centers.
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