In this study, a novel configuration for luminescent solar concentrator photovoltaic (LSC PV) devices is presented, with vertically placed bifacial PV solar cells made of mono-crystalline silicon (mono c-Si). This LSC PV device comprises multiple rectangular cuboid lightguides, made of poly (methyl methacrylate) (PMMA), containing Lumogen dyes, in particular, either Lumogen red 305 or orange 240. The bifacial solar cells are located in between these lightguide cubes and can, therefore, receive irradiance at both of their surfaces. The main aim of this study is to theoretically determine the power conversion efficiency (PCE) of five differently configured LSC PV devices. For this purpose, Monte Carlo ray tracing simulations were executed to analyze the irradiance at receiving PV cell surfaces, as well as the optical performance of these LSC PV devices. Five different LSC PV devices, with different geometries and varying dye concentrations, were modeled. To maximize the device efficiency, the bifacial cells were also attached to the back side of the lightguides. The ray tracing simulations resulted in a maximum efficiency of 16.9% under standard test conditions (STC) for a 15 x 15 cm2 LSC PV device, consisting of nine rectangular cuboid 5 x 5 x 1 cm3 PMMA lightguides with 5 ppm orange 240 dye, with 12 vertically positioned 5 x 1 cm2 bifacial cells in between the lightguides and nine 5 x 5 cm2 PV cells attached to the back of the device. If the cells are not applied to the back of this LSC PV device configuration, the maximum PCE will be 2.9% (under STC), where the LSC PV device consists of 25 cubical 1 x 1 x 1 cm3 PMMA lightguides with 110 ppm red 305 dye and 40 vertically oriented bifacial PV cells of 1 x 1 cm2 in between the lightguides. These results show the vast future potential for LSC PV technologies, with a higher performance and efficiency than the common threshold PCE for LSC PV devices of 10%.