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About: Binary icosahedral group     Goto   Sponge   NotDistinct   Permalink

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In mathematics, the binary icosahedral group 2I or ⟨2,3,5⟩ is a certain nonabelian group of order 120.It is an extension of the icosahedral group I or (2,3,5) of order 60 by the cyclic group of order 2, and is the preimage of the icosahedral group under the 2:1 covering homomorphism of the special orthogonal group by the spin group. It follows that the binary icosahedral group is a discrete subgroup of Spin(3) of order 120. It should not be confused with the full icosahedral group, which is a different group of order 120, and is rather a subgroup of the orthogonal group O(3).