For example, the first isomorphism theorem is a commutative triangle as follows:

Since *f* = *h* ^{o} φ, the left diagram is commutative; and since φ = *k* ^{o} *f*, so is the right diagram.

Similarly, the square above is commutative if *y* ^{o} *w* = *z* ^{o} *x*.

Commutativity makes sense for a polygon of any finite number of sides (including just 1 or 2), and a diagram is commutative if every polygonal subdiagram is commutative.