**Platonic Solids Formulas**

Edge: a

Radius of inscribed circle: r

Radius of circumscribed circle: R

Surface area: S

Volume: V

**There are five Platonic Solids**

The platonic solids are convex polyhedral with equivalent faces composed of congruent convex regular polygons.

Solid | Number of Vertices | Number of Edges | Number of Faces | Section |

Tetrahedron | 4 | 6 | 4 | 3.25 |

Cube | 8 | 12 | 6 | 3.22 |

Octahedron | 6 | 12 | 8 | 3.27 |

Icosahedron | 12 | 30 | 20 | 3.27 |

Dodecahedron | 20 | 30 | 12 | 3.27 |

**Octahedron**

1. r =

2. R =

3. S =

4. V =

**Icosahedron**

1.

2.

3.

4.

**Dodecahedron**

1.

2.

3.

4.