In geometry, an **Archimedean solid** is a convex shape which is composed of polygons. It is a polyhedron, with the following properties:

- Each face is made of a regular polygon
- All the corners of the shape look the same
- The shape is neither a platonic solid, nor a prism, nor an antiprism.

Depending on the way there are counted, there are thirteen or fifteen such shapes. Of two of these shapes, there are two versions, which cannot be made congruent using rotation. The Archimedean solids are named after the Ancient Greek mathematician Archimedes, who probably discovered them in the 3rd century BC. The writings of Archimedes have been lost, but Pappus of Alexandria summarized them in the 4th century. During the Renaissance, artists and mathematicians valued *pure forms* and rediscovered all of these forms. Johannes Kepler probably completed this search around 1620.

Constructing an Archimedean solid takes at least two different polygons.

## Properties

- Archimedean solids are made of regular polygons, therefore all edges have the same length.
- All Archimedean solids can be produced from Platonic solids, by "cutting the edges" of the platonic solid.
- The type of polygons meting at a corner ("vertex") characterizes both the archimedean and platonic solid

## Relationship with Platonic solids

Platonic solids can be turned into Archimedean solids by following a series of rules for their construction.

## Listing of Archimedean solids

The following is a listing of all Archimedean solids

Image | Name | Faces | Type | Edges | Vertices |
---|---|---|---|---|---|

Truncated tetrahedron | 8 | 4 triangles
4 hexagons |
18 | 12 | |

<Cuboctahedron | |||||

Cubocthahedron | 14 | 8 triangles
6 squares |
24 | 12 | |

Truncated cube | 14 | 8 triangles
6 octagons |
36 | 24 | |

Truncated octahedron | 14 | 6 squares
8 hexagons |
36 | 24 | |

Rhombicuboctahedron | 26 | 8 triangles
18 squares |
48 | 24 | |

Truncated cuboctahedron | 26 | 12 squares
8 hexagons 6 octagons |
72 | 48 | |

Snub cube (2 mirrored versions) | 38 | 32 triangles
6 squares |
60 | 24 | |

Icosidodecahedron | 32 | 20 triangles
12 pentagons |
60 | 30 | |

Truncated dodecahedron | 32 | 20 triangles
12 decagons |
90 | 60 | |

Truncated icosahedron | 32 | 12 pentagons
20 hexagons |
90 | 60 | |

Rhombicosidodecahedron | 62 | 20 triangles 30 squares 12 pentagons |
120 | 60 | |

Truncated icosidodecahedron | 62 | 30 squares
20 hexagons 12 decagons |
180 | 120 | |

Snub dodecahedron (2 mirrored versions) | 92 | 80 triangles
12 pentagons |
150 | 60 |

*Kiddle Encyclopedia.*