Binary icosahedral group Totally Explained

Everything about Binary Icosahedral Group totally explained

In mathematics, the binary icosahedral group is an extension of the icosahedral group I of order 60 by a cyclic group of order 2. It can be defined as the preimage of the icosahedral group under the 2:1 covering homomorphism:

mathrm.

Various other 4-dimensional symmetry groups can be constructed from 2I. For details, see (Conway and Smith, 2003).

Applications

The coset space Sp(1)/2I is a spherical 3-manifold called the Poincaré homology sphere. It is an example of a homology sphere, for example a 3-manifold whose homology groups are identical to those of a 3-sphere. The fundamental group of the Poincaré sphere is isomorphic to the binary icosahedral group.

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