For Hamilton's use of icosian, see icosian game and icosian calculus.
Specific set of Hamiltonian quaternions with the same symmetry as the 600-cell
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In mathematics, the icosians are a specific set of Hamiltonian quaternions with the same symmetry as the 600-cell. The term can be used to refer to two related, but distinct, concepts:
The icosian group: a multiplicative group of 120 quaternions, positioned at the vertices of a 600-cell of unit radius. This group is isomorphic to the binary icosahedral group of order 120.
The icosian ring: all finite sums of the 120 unit icosians.
The icosian game is a mathematical game invented in 1856 by Irish mathematician William Rowan Hamilton. It involves finding a Hamiltonian cycle on a dodecahedron...
icosian ring: all finite sums of the 120 unit icosians. The 120 unit icosians, which form the icosian group, are all even permutations of: 8 icosians...
The icosian calculus is a non-commutative algebraic structure discovered by the Irish mathematician William Rowan Hamilton in 1856. In modern terms, he...
paths and cycles are named after William Rowan Hamilton, who invented the icosian game, now also known as Hamilton's puzzle, which involves finding a Hamiltonian...
intervals, in the Philosophical Magazine. Hamilton also introduced the icosian game or Hamilton's puzzle. It is based on the concept of a Hamiltonian...
lattice that is constructed with one hundred and twenty quaternionic unit icosians that make up the vertices of the 600-cell, whose Euclidean norms define...
integers. The Leech lattice can also be constructed using the ring of icosians. The icosian ring is abstractly isomorphic to the E8 lattice, three copies of...
Baron Kelvin. 1851: Binaural stethoscope created by Arthur Leared. 1856: Icosian calculus discovered by Sir William Rowan Hamilton. 1859: Greenhouse Effect...
constructed using the octonions as well as with three copies of the ring of icosians that are isomorphic to the E 8 {\displaystyle \mathrm {E} _{8}} lattice...
given by the Irish mathematician William Rowan Hamilton in 1856, in his icosian calculus, where he discovered an order two automorphism, writing: so that...
quaternions and octonions. Together with Neil Sloane, he invented the icosians. He invented a base 13 function as a counterexample to the converse of...
presentation was given by William Rowan Hamilton in 1856, in his paper on icosian calculus. Note that other presentations are possible, for instance as an...
history of combinatorial group theory. A proto-form is found in the 1856 icosian calculus of William Rowan Hamilton, where he studied the icosahedral symmetry...
red-haired typists 1957 May About the remarkable similarity between the Icosian Game and the Tower of Hanoi 1957 Jun Curious figures descended from the...
given by the Irish mathematician William Rowan Hamilton in 1856, in his icosian calculus – a presentation of the icosahedral group. The first systematic...
1860, and 1864. Happy Families – popular card game, developed in 1851. Icosian game – a mathematical puzzle involving cycles on a dodecahedron, invented...
from a mathematical game invented in 1857 by William Rowan Hamilton, the icosian game. The game's object was to find a Hamiltonian cycle along the edges...
for the greatest common divisor. Gaussian integer Eisenstein integer The icosians The Lie group F4 The E8 lattice Conway & Smith 2003, p. 56 Conway, John...
Rowan Hamilton and by the British mathematician Thomas Kirkman. Hamilton's icosian game was a recreational puzzle based on finding a Hamiltonian cycle. The...
Felix Klein, in the early 1880s, while an early form is found in the 1856 icosian calculus of William Rowan Hamilton, where he studied the icosahedral symmetry...
graph, is named after Herschel due to his pioneering work on Hamilton's Icosian game. The second son and fifth child of Sir John and Lady Margaret Herschel's...
multiply as the binary octahedral group. Another subgroup is formed by 120 icosians which multiply in the manner of the binary icosahedral group. A hyperbolic...
regular 600 cell with Schläfli symbol {3,3,5} can be taken as the unit icosians, corresponding to the double cover of the rotational symmetry group of...
Representing rotations with quaternions, I is made up of the 120 unit icosians. As before, this is a 1-to-2 correspondence. Ih, (*532) [5,3] () 532/m...
3,5) triangle group by William Rowan Hamilton in 1856, in his paper on icosian calculus. Triangle groups arise in arithmetic geometry. The modular group...
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