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In photomultiplier-quadrant-sharing (PQS) geometry for positron emission tomography applications, each PMT is shared by four blocks and each detector block is optically coupled to four round PMTs. Although this design reduces the cost of high-resolution PET systems, when the camera consists of detector panels that are made up of square blocks, half of the PMT's sensitive window remains unused at the detector panel edge. Our goal was to develop a LYSO detector panel which minimizes the unused portion of the PMTs for a low-cost, high-resolution, and high-sensitivity positron emission mammography (PEM) camera. We modified the PQS design by using elongated blocks at panel edges and square blocks in the inner area. For elongated blocks, symmetric and asymmetrical reflector patterns were developed and PQS and PMT-half-sharing (PHS) arrangements were implemented in order to obtain a suitable decoding. The packing fraction was 96.3% for asymmetric block and 95.5% for symmetric block. Both of the blocks have excellent decoding capability with all crystals clearly identified, 156 for asymmetric and 144 for symmetric and peak-to-valley ratio of 3.0 and 2.3 respectively. The average energy resolution was 14.2% for the asymmetric block and 13.1% for the symmetric block. Using a modified PQS geometry and asymmetric block design, we reduced the unused PMT region at detector panel edges, thereby increased the field-of-view and the overall detection sensitivity and minimized the undetected breast region near the chest wall. This detector design and using regular round PMT allowed building a lower-cost, high-resolution and high-sensitivity PEM camera.