Abstract

According to a recent theory the Universe could be a dodecahedron. It is surprising that Plato used a dodecahedron as the quintessence to describe the cosmos. In this paper we will prove the shape of the Universe is Poincaré dodecahedral space. From the dimensionless unification of the fundamental interactions will propose a possible solution for the density parameter of baryonic matter,dark matter and dark energy. The sum of the contributions to the total density parameter at the current time is Ω0=1,0139. This result answers the ancient question of whether space is finite or infinite,while retaining the standard Friedmann-Lemaître foundation for local physics.