Associativity : The associativity axiom deals with composing more than two symmetries: Starting with three elements ⁠ a ⁠, ⁠ b ⁠ and ⁠ c ⁠ of ⁠ D 4 ⁠, there are two possible ways of using these three symmetries in this order to determine a symmetry of the square. One of these ways is to first compose a and b into a single symmetry, then to compose that symmetry with ⁠ c ⁠. The other way is to first compose b and ⁠ c ⁠, then to compose the resulting symmetry with ⁠ a ⁠. These two ways must give always the same result, that is, ( a ∘ ∘ b ) ∘ ∘ c = a ∘ ∘ ( b ∘ ∘ c ) , For example, ( f d ∘ ∘ f v ) ∘ ∘ r 2 = f d ∘ ∘ ( f v ∘ ∘ r 2 ) can be checked using the Cayley table: ( f d ∘ ∘ f v ) ∘ ∘ r 2 = r 3 ∘ ∘ r 2 = r 1 f d ∘ ∘ ( f v ∘ ∘ r 2 ) = f d ∘ ∘ f h = r 1 .