A combined discontinuous molecular dynamics and Monte Carlo simulation technique is used to study the swelling of athermal, continuous-space, near-perfect, trifunctional polymer networks containing hard chains of lengths 20 and 35 immersed in an athermal hard-sphere solvent. The swelling simulations are conducted under conditions of constant pressure and chemical potential. A simple, analytical theory for gel swelling is presented in which the gel free energy is calculated as the sum of an elastic, affine-type term, and a liquidlike mixing term that is based on the generalized-Flory dimer equation of state. The theory shows good agreement with our simulation results for the gel properties at swelling equilibrium.