The search for new superconducting materials has been spurred on by the discovery of iron-based superconductors whose structure and composition is qualitatively different from the cuprates. The study of one such material, KxFe2-ySe2 with a critical temperature of 32 K, is made more difficult by the fact that it separates into two phases-a dominant antiferromagnetic insulating phase K2Fe4Se5, and a minority superconducting phase whose precise structure is as yet unclear. Here we perform electrical and magnetization measurements, scanning electron microscopy and microanalysis, X-ray diffraction and scanning tunnelling microscopy on KxFe2-ySe2 crystals prepared under different quenching processes to better understand the relationship between its microstructure and its superconducting phase. We identify a three-dimensional network of superconducting filaments within this material and present evidence to suggest that the superconducting phase consists of a single Fe vacancy for every eight Fe-sites arranged in a √8 x √10 parallelogram structure.