Elements
Explicitly, the binary octahedral group is given as the union of the 24 Hurwitz units
with all 24 quaternions obtained from
by a permutation of coordinates (all possible sign combinations). All 48 elements have absolute value 1 and therefore lie in the unit quaternion group Sp(1).
Read more about this topic: Binary Octahedral Group
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—Herman Melville (1819–1891)
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