Platonic Solids and Euler’s Formula

This section covers the five Platonic Solids and their properties, which are common topics on tests. You should memorize the number of faces, vertices, and edges for each.

• Tetrahedron: 4 triangular faces, 4 vertices, 6 edges
• Cube (Hexahedron): 6 square faces, 8 vertices, 12 edges
• Octahedron: 8 triangular faces, 6 vertices, 12 edges
• Dodecahedron: 12 pentagonal faces, 20 vertices, 30 edges
• Icosahedron: 20 triangular faces, 12 vertices, 30 edges

If you forget one property, you can use Euler's Formula to find it: Faces + Vertices - Edges = 2.