  We show that the variety of symmetric implication algebras is generated from
cubic implication algebras and Boolean algebras. We do this by developing the
notion of a locally symmetric implication algebra that has properties similar
to cubic implication algebras and provide a representation of these algebras as
subalgebras of a product of a cubic implication algebra and an implication
algebra. We then show that every symmetric implication algebra is covered by a
locally symmetric implication algebra.
