Two-dimensional carbon allotropes have attracted much attention due to their extraordinary optoelectronic and mechanical properties, which can be exploited for energy conversion and storage applications. In this work, we use density functional theory simulations and semi-empirical methods to investigate the mechanical, thermoelectric, and excitonic properties of Tetrahexcarbon (also known as Tetragraphene). This quasi-2D carbon allotrope exhibits a combination of squared and hexagonal rings in a buckled shape. Our findings reveal that tetragraphene is a semiconductor material with a direct electronic bandgap of 2.66eV. Despite the direct nature of the electronic band structure, this material has an indirect exciton ground state of 2.30eV, which results in an exciton binding energy of 0.36eV. At ambient temperature, we obtain that the lattice thermal conductivity (κL) for tetragraphene is approximately 118 W/mK. Young’s modulus and the shear modulus of tetragraphene are almost isotropic, with maximum values of 286.0N/m and 133.7N/m, respectively, while exhibiting a very low anisotropic Poisson ratio value of 0.09.