A system for sensing multiple local electric voltages from endocardial surface of a heart, includes: an elongate tubular member; a plurality of flexible splines having proximal portions, distal portions and medial portions therein between; an anchor for securably affixing the proximal portions of the splines; a tip for securably affixing the distal portions of the splines; and a polymeric member including opposed a first open end and a second open end defining an open lumen therein between and an inner member surface and an outer member surface, wherein at least one of the plurality of flexible splines is at least partially disposed within the lumen of the polymeric member; a flexible electrode assembly strip with one or more exposed electrodes disposed on at least a portion of the outer surface of the polymeric member.