Icosian (original) (raw)
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.
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| dbo:abstract | 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. (en) En matemáticas, los icosianos son un conjunto específico de cuaterniones Hamiltonianos con la misma simetría que el hexacosicoron. El término puede ser utilizado para referirse a dos términos relacionados, pero distintos: * El grupo icosiano: un grupo multiplicativo de 120 cuaterniones, posicionados en los vértices de un hexacosicoron de radio 1. Este grupo es isomórfico al grupo icosaédrico binario de orden 120. * El anillo icosiano: todas las sumas finitas del icosiano de 120 unidades (es) |
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| rdfs:comment | 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. (en) En matemáticas, los icosianos son un conjunto específico de cuaterniones Hamiltonianos con la misma simetría que el hexacosicoron. El término puede ser utilizado para referirse a dos términos relacionados, pero distintos: * El grupo icosiano: un grupo multiplicativo de 120 cuaterniones, posicionados en los vértices de un hexacosicoron de radio 1. Este grupo es isomórfico al grupo icosaédrico binario de orden 120. * El anillo icosiano: todas las sumas finitas del icosiano de 120 unidades (es) |
| rdfs:label | Icosiano (es) Icosian (en) |
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