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Superconducting triplet quadrupoles (STQs) with large apertures and high field-gradients are employed for the in-flight radioactive-isotope (RI) beam separator BigRIPS at RIKEN. It consists of fourteen STQs and six room-temperature dipoles. The use of the STQs makes it possible to achieve important features of the BigRIPS separator: large acceptances and a large magnetic rigidity, allowing efficient production of RI beams. The BigRIPS separator is presently under construction and assembly as a major installation in the RIKEN RI-beam factory project, and the commissioning is scheduled in early 2007. In this paper we present the status and overview of the BigRIPS separator, emphasizing the STQs and their liquid-helium cryogenic systems.