Archimedean Solids

Semi-regular polyhedra with uniform vertices and multiple face types

Truncated Solids

Truncated Tetrahedron

Truncated tetrahedron - 4 triangles and 4 hexagons

Truncated Cube

Truncated cube - 8 triangles and 6 octagons

Truncated Octahedron

Truncated octahedron - 6 squares and 8 hexagons

Truncated Dodecahedron

Truncated dodecahedron - 20 triangles and 12 decagons

Truncated IcosahedronSoccer Ball

Truncated icosahedron - 12 pentagons and 20 hexagons (soccer ball)

Composite Forms

Cuboctahedron

Combination of cube and octahedron - 8 triangles and 6 squares

Icosidodecahedron

Combination of icosahedron and dodecahedron - 20 triangles and 12 pentagons

Truncated Cuboctahedron

Truncated cuboctahedron - 12 squares, 8 hexagons, 6 octagons

Truncated Icosidodecahedron

Truncated icosidodecahedron - 30 squares, 20 hexagons, 12 decagons

Rhombic Forms

Rhombicuboctahedron

Extended form - 8 triangles and 18 squares

Rhombicosidodecahedron

Extended form - 20 triangles, 30 squares, 12 pentagons

Snub Forms (Chiral)

Snub Cube Chiral

Twisted form of the cube - 32 triangles and 6 squares

Snub Dodecahedron Chiral

Twisted form of the dodecahedron - 80 triangles and 12 pentagons

About Archimedean Solids

The Archimedean solids are semi-regular polyhedra with uniform vertices but different regular polygons as faces:

Architecture - Geodesic structures
Crystallography - Complex crystal forms
Chemistry - Fullerenes and molecules

Game Design - Special dice
Sports - Soccer ball form
Art - Sculptures and design

Properties of Archimedean Solids

Semi-Regularity

All vertices are identical
Different regular face types

Construction

By truncation of Platonic solids
Or by cantellation

Chirality

Snub forms exist in two mirror forms
Left- and right-handed versions

Completeness

Exactly 13 Archimedean solids
Plus 2 prismatic families

Special Feature: The truncated icosahedron is the geometric form of a soccer ball with 12 black pentagons and 20 white hexagons.

Quick Reference

13 Solids

Archimedean Solids

Uniform

Vertices

Mixed

Faces

2 Chiral

Snub Forms

⚽

Soccer Ball

Historical Context

Archimedes (287-212 BC): Discovered these semi-regular polyhedra as a complement to the Platonic solids.

Johannes Kepler (1619): Systematically described the Archimedean solids in "Harmonices Mundi".

Buckminster Fuller (20th century): Revolutionized architecture with geodesic domes.