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A $d$-dimensional simplicial complex is balanced if the underlying graph is$(d+1)$-colorable. We present an implementation of cross-flips, a set of localmoves introduced by Izmestiev, Klee and Novik which connect any twoPL-homeomorphic balanced combinatorial manifolds. As a result we exhibit avertex minimal balanced triangulation of the real projective plane, of thedunce hat and of the real projective space, as well as several balancedtriangulations of surfaces and 3-manifolds on few vertices. In particular weconstruct small balanced triangulations of the 3-sphere that are non-shellableand shellable but not vertex decomposable.

Balanced triangulations on few vertices and an implementation of cross-flips