The set of octonions, also sometimes called Cayley numbers and denoted , consists of the elements in a Cayley algebra. A typical octonion is of the form
where each of the triples , , , , , , behaves like the quaternions . Octonions are not associative. They have been used in the study of eight-dimensional space, in which a general rotation can be written as
More things to try:
Weisstein, Eric W. "Octonion." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Octonion.html