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
Famous quotes containing the word elements:
“In spite of all their kind some elements of worth
With difficulty persist here and there on earth.”
—Hugh MacDiarmid (1892–1978)
“The two elements the traveler first captures in the big city are extrahuman architecture and furious rhythm. Geometry and anguish. At first glance, the rhythm may be confused with gaiety, but when you look more closely at the mechanism of social life and the painful slavery of both men and machines, you see that it is nothing but a kind of typical, empty anguish that makes even crime and gangs forgivable means of escape.”
—Federico García Lorca (1898–1936)
“Icebergs behoove the soul
(both being self-made from elements least visible
to see them so; fleshed, fair, erected indivisible.”
—Elizabeth Bishop (1911–1979)