We present a revised strong lensing mass reconstruction of the galaxy cluster RX J1347.5-1145. The X-ray luminous cluster at redshift z=0.451 has already been studied intensively in the past. Based on information of two such previous (strong-)lensing studies by Halkola et al. (2008) and Bradac et al. (2008), as well as by incorporating newly available data from the Cluster Lensing And Supernovae survey with Hubble (CLASH, Postman et al. 2012), we identified four systems of multiply lensed images (anew) in the redshift range 1.75 <= z <= 4.19. One multiple image system consists of in total eight multiply lensed images of the same source. The analysis based on a parametric mass model derived with the software glafic (Oguri 2010) suggests that the high image multiplicity is due to the source (z_phot = 4.19) being located on a so-called swallowtail caustic. In addition to the parametric mass model, we also employed a non-parametric approach using the software PixeLens (Saha and Williams 1997, 2004) in order to reconstruct the projected mass of the cluster using the same strong lensing data input. Both reconstructed mass models agree in revealing several mass components and a highly elliptic shape of the mass distribution. Furthermore, the projected mass inside, for example, a radius R ~35 arcsec ~200 kpc of the cluster for a source at redshift z=1.75 obtained with PixeLens exceeds the glafic estimate within the same radius by about 13 per cent. The difference could be related to the fundamental degeneracy involved when constraining dark matter substructures with gravitationally lensed arcs.
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