Rotational symmetry | Abstract algebra | Graph theory | Binary operations

Icosian calculus

The icosian calculus is a non-commutative algebraic structure discovered by the Irish mathematician William Rowan Hamilton in 1856.In modern terms, he gave a group presentation of the icosahedral rotation group by generators and relations. Hamilton's discovery derived from his attempts to find an algebra of "triplets" or 3-tuples that he believed would reflect the three Cartesian axes. The symbols of the icosian calculus can be equated to moves between vertices on a dodecahedron. Hamilton's work in this area resulted indirectly in the terms Hamiltonian circuit and Hamiltonian path in graph theory. He also invented the icosian game as a means of illustrating and popularising his discovery. (Wikipedia).

Icosian calculus
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Related pages

Algebraic structure | Combinatorial group theory | Hamiltonian path | Icosian | Group (mathematics) | Alternating group | Dodecahedron | William Rowan Hamilton | Generating set of a group | Icosahedron | Cartesian coordinate system | Coxeter group | Dessin d'enfant | Geometric group theory | Tuple | Icosian game | Triangle group | Directed graph | Presentation of a group