Polyhedron Explorer – Instructional Edition

Overview of Polyhedra

Polyhedra are three-dimensional solids with flat polygonal faces, straight edges, and vertices. In this lesson we focus on five common polyhedra:

  1. Cube: All faces are squares.
  2. Tetrahedron: 4 triangular faces.
  3. Octahedron: 8 triangular faces.
  4. Dodecahedron: 12 pentagonal faces.
  5. Icosahedron: 20 triangular faces.

Key Formulas

Cube: Volume = a³, Surface Area = 6a²

Tetrahedron: Volume = a³/(6√2), Surface Area = √3·a²

Octahedron: Volume = (√2/3)·a³, Surface Area = 2√3·a²

Dodecahedron: Volume = ((15+7√5)/4)·a³, Surface Area = 3√(25+10√5)·a²

Icosahedron: Volume = [5(3+√5)/12]·a³, Surface Area = 5√3·a²

This application will allow you to compute these values based on an input edge length and test your understanding with a quiz. In this edition, we focus entirely on detailed explanations and calculations—no 3D images are required.

Polyhedron Calculator



Polyhedron Quiz