Icosahedral Group

Some articles on group, icosahedral group, groups:

600-cell - Coordinates
... When interpreted as quaternions, the 120 vertices of the 600-cell form a group under quaternionic multiplication ... This group is often called the binary icosahedral group and denoted by 2I as it is the double cover of the ordinary icosahedral group I ... It occurs twice in the rotational symmetry group RSG of the 600-cell as an invariant subgroup, namely as the subgroup 2IL of quaternion left-multiplications and as the subgroup 2IR of ...
Point Groups In Three Dimensions - Binary Polyhedral Groups
... The map Spin(3) → SO(3) is the double cover of the rotation group by the spin group in 3 dimensions ... subgroups of Spin(3) and subgroups of SO(3) (rotational point groups) the image of a subgroup of Spin(3) is a rotational point group, and the preimage of a point group is a subgroup of Spin(3) ... The preimage of a finite point group is called a binary polyhedral group, represented as , and is called by the same name as its point group, with the prefix binary, with double the order of ...

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