# Polyhedra

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## Last revised 2003-02-22

There are five regular polyhedra. They are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron.

### The Tetrahedron

The tetrahedron is composed of four equilateral triangles.

### The Cube

**
Schläfli symbol**: {4,3}

Dual: Octahedron

**
Surface Area**: 6a^{2}

Volume: a^{3}

**Vertices**: 6, **Edges**: 12, **Faces**: 8

The cube is composed of six squares.

### The Octahedron

**
Schläfli symbol**: {8,3}

Dual: Cube

**
Surface Area**: 2a^{2}√3

Volume: (1/3)a^{3}√2

**Vertices**: 6, **Edges**: 12, **Faces**: 8

The octahedron is composed of eight equilateral triangles.

### The Dodecahedron

**
Schläfli symbol**: {5,3}

Dual: Icosahedron

**
Surface Area**: 3a^{2}√(25 + 10√5))

Volume: (1/4)a^{3}(15 + √5)

**Vertices**: 20, **Edges**: 30, **Faces**: 12

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The dodecahedron is composed of twelve pentagons.

### The Icosahedron

**
Schläfli symbol**: {3,5}

Dual: Dodecahedron

**
Surface Area**: 5a^{2}√3

Volume: (5/12)a^{3}(3 + √5)

**Vertices**: 12, **Edges**: 20, **Faces**: 20

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The icosahedron is composed of twenty equilateral triangles.

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