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In algebra, a triple system is a [[vector space]] $V$ over a field $K$ with a [[ternary operation]] which is a $K$-[[trilinear mapping]] $V \times V \times V \rightarrow V$.  Examples include [[Freudenthal–Kantor triple system]]s, [[Jordan triple system]]s, [[Lie triple system]]s, [[Anti-Lie triple system]]s and [[Allison-Hein triple system]]s.  

In combinatorics, a triple system is a class of [[block design]] with blocks of size $3$.  Examples include [[Steiner triple system]] and [[Kirkman triple system]].

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