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Mathematical Origami

Platonic Solids

Platonic Solids are the most regular polyhedra: all faces the the same regular polygon, and they look the same at every vertex. The Greek philosopher Plato discovered that there are only five solids with these properties. He belied that the they correspond to the four ancient Elements, Earth, Water, Air and Fire, as well as the Universe.

Tetrahedron

Cube

Octahedron

Dodecahedron

Icosahedron

Archimedean Solids

Archimedean Solids, like the Platonic ones, consist of regular Polygons and look the same at every vertex. However the faces are multiple different regular polygons. There are 13 Archimedean Solids, two of which are reflections of each other.

Truncated Tetrahedron

Cuboctahedron

Truncated Hexahedron

Truncated Octahedron

Rhombicuboctahedron

Truncated Cuboctahedron

Snub Cube

Icosidodecahedron

Truncated Dodecahedron

Truncated Icosahedron

Rhombicosidodecahedron

Truncated Icosidodecahedron

Snub Dodecahedron

Stars and Compounds

Beautiful Origami

Further Reading

Polygons and PolyhedraMathematics of Paper Folding