Pelayo, A.Pires, A. R.Ratiu, T. S.Sabatini, S.2014-05-022014-05-022014-05-02201410.1007/s10711-013-9858-xhttps://infoscience.epfl.ch/handle/20.500.14299/103097WOS:000332790500021We construct a distance on the moduli space of symplectic toric manifolds of dimension four. Then we study some basic topological properties of this space, in particular, path-connectedness, compactness, and completeness. The construction of the distance is related to the Duistermaat-Heckman measure and the Hausdorff metric. While the moduli space, its topology and metric, may be constructed in any dimension, the tools we use in the proofs are four-dimensional, and hence so is our main result.Toric manifoldDelzant polytopeModuli spaceMetric spacetext::journal::journal article::research article