Thermodynamic properties of confined systems depend on sizes of the confinement domain due to quantum nature of particles. It is shown that shape also enters as a control parameter on thermodynamic state functions. Here we consider a nanoscale confinement domain that is specially arranged to reveal quantum shape effects. By creating a size preserved shape transformation, we investigate purely quantum shape effects without having any influence from size effects. In this project, we consider degenerate Fermi gases confined in specially arranged 1D, 2D and 3D domains. First we solve Schrödinger equation for the particles in these various dimensional confinement domains. Then we calculate partition function, free energy, internal energy, entropy and specific heat capacity and examine the quantum shape dependence of these quantities explicitly. Entropy and heat capacity already show quantum oscillations due to variations in size and carrier concentration. We expect shape variation to lead additional quantum oscillations in these quantities and possibly in other thermodynamic quantities as well. Shape dependence introduces a new degree of freedom to manipulate and tailor the thermodynamic properties of confined systems. By exploring how shape dependence modifies thermodynamic properties, it may be possible to design new nanoscale devices with favorable features based on quantum shape effects.