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sedenion

In abstract algebra, the sedenions form a 16-dimensional noncommutative and nonassociative algebra over the real numbers, usually represented by the capital letter S, boldface $S$ or blackboard bold ${\\displaystyle \\mathbb {S} }$ . They are obtained by applying the Cayley–Dickson construction to the octonions, and as such the octonions are isomorphic to a subalgebra of the sedenions. Unlike the octonions, the sedenions are not an alternative algebra. Applying the Cayley–Dickson construction to the sedenions yields a 32-dimensional algebra, sometimes called the 32-ions or trigintaduonions. It is possible to continue applying the Cayley–Dickson construction arbitrarily many times.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Sedenion)

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