We present the first optical (590--890 nm) imaging polarimetry observations of the pre-transitional protoplanetary disk around the young solar analog LkCa 15, addressing a number of open questions raised by previous studies. We detect the previously unseen far side of the disk gap, confirm the highly eccentric scattered-light gap shape that was postulated from near-infrared imaging, at odds with the symmetric gap inferred from millimeter interferometry. Furthermore, we resolve the inner disk for the first time and trace it out to 30 AU. This new source of scattered light may contribute to the near-infrared interferometric signal attributed to the protoplanet candidate LkCa 15 b, which lies embedded in the outer regions of the inner disk. Finally, we present a new model for the system architecture of LkCa 15 that ties these new findings together. These observations were taken during science verification of SPHERE ZIMPOL and demonstrate this facility's performance for faint guide stars under adverse observing conditions.