The question of the universe's shape is a complex and unresolved topic in cosmology. While current measurements suggest that the universe is flat, it could possess one of 18 different shapes. These shapes range from infinitely extended 3D spaces to various compact configurations, such as toroidal forms. Historical studies, such as those by mathematician Carl Friedrich Gauss, laid the groundwork for understanding curvature in space. Observations of the cosmic microwave background radiation, which is the remnant light from the early universe, indicate that matter was evenly distributed, leading to the cosmological principle of homogeneity and isotropy. Recent research has focused on density fluctuations within this radiation to determine the universe's geometry. The COMPACT collaboration, initiated in 2022, is at the forefront of this research, analyzing cosmic data to identify features that could suggest complex shapes. The implications of understanding the universe's shape extend beyond academic interest, as it may illuminate the quantum processes that shaped the cosmos shortly after the Big Bang.