Archimedean Solids
Welcome to the Archimedean Solids Explorer, a journey through the thirteen semi-regular polyhedra that bridge perfect symmetry with beautiful variation. Unlike the Platonic solids, which have identical faces, Archimedean solids feature a fascinating mix of regular polygons arranged in identical patterns around each vertex.
Named after the ancient Greek mathematician Archimedes, who is believed to have described them comprehensively, these solids represent a perfect balance between uniformity and diversity. Each Archimedean solid exhibits a unique arrangement of two or more types of regular polygonal faces, creating forms that have captivated mathematicians, artists, and architects throughout history.
Beyond Perfect Symmetry
The Archimedean solids represent a fascinating middle ground between the perfect regularity of the five Platonic solids and the infinite variety of irregular polyhedra. Their semi-regular nature—featuring different types of regular polygons arranged in identical vertex configurations—gives them unique mathematical properties and visual appeal.
While the Platonic solids represent pure elements and fundamental principles, the Archimedean solids can be seen as embodying transformation and the harmonious blending of different qualities. Many can be derived by "truncating" (cutting off) the vertices of Platonic solids, revealing how new forms of balance and beauty emerge through transformation of simpler structures.
Throughout history, these forms have appeared in art, architecture, and design—from the geometric drawings of Leonardo da Vinci to modern architectural domes. In nature, some viruses and molecular structures display Archimedean symmetry, demonstrating how these mathematical forms manifest in biological systems. From ancient Greece to contemporary science, the Archimedean solids continue to reveal the profound connection between mathematical elegance and natural organization.
Explore The Thirteen Archimedean Solids
Truncated Tetrahedron
4 hexagons, 4 triangles
12 vertices • 18 edges
Cuboctahedron
8 triangles, 6 squares
12 vertices • 24 edges
Truncated Cube
8 triangles, 6 octagons
24 vertices • 36 edges
Truncated Octahedron
6 squares, 8 hexagons
24 vertices • 36 edges
Rhombicuboctahedron
8 triangles, 18 squares
24 vertices • 48 edges
Truncated Cuboctahedron
12 squares, 8 hexagons, 6 octagons
48 vertices • 72 edges
Snub Cube
32 triangles, 6 squares
24 vertices • 60 edges
Icosidodecahedron
20 triangles, 12 pentagons
30 vertices • 60 edges
Truncated Dodecahedron
20 triangles, 12 decagons
60 vertices • 90 edges
Truncated Icosahedron
12 pentagons, 20 hexagons
60 vertices • 90 edges
Rhombicosidodecahedron
20 triangles, 30 squares, 12 pentagons
60 vertices • 120 edges
Truncated Icosidodecahedron
30 squares, 20 hexagons, 12 decagons
120 vertices • 180 edges
Snub Dodecahedron
80 triangles, 12 pentagons
60 vertices • 150 edges