For iterative, fully 3D positron emission tomography (PET) image reconstruction intrinsic symmetries can be used to significantly reduce the size of the system matrix. The precalculation and beneficial memory-resident storage of all nonzero system matrix elements is possible where sufficient compression exists. Thus, reconstruction times can be minimized independently of the used projector and more elaborate weighting schemes, e.g., volume-of-intersection (VOI), are applicable. A novel organization of scanner-independent, adaptive 3D projection data is presented which can be advantageously combined with highly rotation-symmetric voxel assemblies. In this way, significant system matrix compression is achieved. Applications taking into account all physical lines-of-response (LORs) with individual VOI projectors are presented for the Siemens ECAT HR+ whole-body scanner and the Siemens BrainPET, the PET component of a novel hybrid-MR/PET imaging system. Measured and simulated data were reconstructed using the new method with ordered-subset-expectation-maximization (OSEM). Results are compared to those obtained by the sinogram-based OSEM reconstruction provided by the manufacturer. The higher computational effort due to the more accurate image space sampling provides significantly improved images in terms of resolution and noise.