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A two-dimensional simplicial complex is called $d$-{\em regular} if everyedge of it is contained in exactly $d$ distinct triangles. It is called$\epsilon$-expanding if its up-down two-dimensional random walk has anormalized maximal eigenvalue which is at most $1-\epsilon$.  In this work, we present a class of bounded degree 2-dimensional expanders,which is the result of a small 2-complex action on a vertex set. The resultedcomplexes are fully transitive, meaning the automorphism group actstransitively on their faces.  Such two-dimensional expanders are rare! Known constructions of such boundeddegree two-dimensional expander families are obtained from deep algebraicreasonings (e.g. coset geometries).  We show that given a small $d$-regular two-dimensional $\epsilon$-expander,there exists an $\epsilon'=\epsilon'(\epsilon)$ and a family of bounded degreetwo-dimensional simplicial complexes with a number of vertices goes toinfinity, such that each complex in the family satisfies the followingproperties:  * It is $4d$-regular.  * The link of each vertex in the complex is the same regular graph (up toisomorphism).  * It is $\epsilon'$ expanding.  * It is transitive.  The family of expanders that we get is explicit if the one-skeleton of thesmall complex is a complete multipartite graph, and it is random in the case of(almost) general $d$-regular complex. For the randomized construction, we useresults on expanding generators in a product of simple Lie groups. Thisconstruction is inspired by ideas that occur in the zig-zag product for graphs.It can be seen as a loose two-dimensional analog of the replacement product.

Transitive bounded-degree 2-expanders from regular 2-expanders