As part of the PALADIN project which aims to develop a gamma photon detector with 100 ps FWHM time resolution, 1mm FWHM spatial resolution, 10 % FWHM energy resolution and a detection efficiency of about 90%, this thesis aims to provide an accurate simulation of the proposed detector system and to enable a first analysis of its properties. The new design features a central cube shaped scintillation crystal with its sides in direct optical contact to up to 6 dSiPMs developed by Philips. The goal is to improve on current designs in terms of spatial and temporal resolution, energy resolution and photon detection efficiency. To this end, a GEANT4 (GEometry ANd Tracking) application was developed in this work to simulate the new detector system and produce output of resulting scintillation photon emissions from 511keV annihilation photons interacting with a monolithic LYSO:Ce:Ca (Lutetium Yttrium Oxy-Orthosilicate, co-doped with Cerium and Calcium) scintillation crystal. The goal of the simulations presented in this thesis is to determine whether or not the new detector system can be expected to improve on already existing designs where only one or two DPCs were used for readout. These older designs showed, i.e., varying performance for spatial reconstruction along different directions which was inherent in their asymmetric design. Possible improvements in performance for the 6-sided readout will be studied by first discussing the plausibility of the data and then analyzing a few first results such as the probabilities of various processes, the distribution of detection times for photons, the number of Cherenkov photons produced per event, and the performance of a spatial reconstruction algorithm. The data analysis is performed with a self developed ROOT script.