The 13 Archimedean Solids

What are they?

Archimedean solids are related to the five Platonic Solids. Remember that the Platonic solids are the only regular, convex solids. What happens if we loosen the constraint of regularity?

Instead of requiring that the faces meeting at a vertex be the same polygon, we now require that

• the faces meeting at a vertex all be regular polygons, not necessarily the same ones
• the polyhedron be uniform, thus every vertex must still be equivalent (the faces occur in the same order about each vertex)
• the polyhedron be convex
• any vertex can be moved into the position of any other vertex by rotating or reflecting the polyhedron

Archimedean solids obtained by truncating Platonic solids

Truncation means cutting off the corners of a solid. We cut off identical lengths along each edge emerging from a vertex. This process adds a new face to the polyhedron. Each of the following pages explains the process in more detail.

Truncated Tetrahedron
Truncated Cube
Truncated Octahedron
Truncated Icosahedron
Truncated Dodecahedron

Cuboctahedron
Icosidodecahedron

Archimedean solids obtained by truncating other Archimedean Solids

If we truncate the cuboctahedron or the icosidodecahedron, we will obtain four more solids.

Rhombitruncated Cuboctahedron
Rhombicuboctahedron

Rhombitruncated Icosidodecahedron
Rhombicosidodecahedron

Archimedean solids obtained by "snubbing" Platonic Solids