Computer simulations are an important tool for linking the behaviour of polymer materials to the properties of the constituent polymer chains. In simulations, one normally uses periodic boundary conditions to mimic a macroscopic system. For a cross-linked polymer network, this will impose restrictions on the motion of the polymer chains at the borders of the simulation cell. We present a new method for constructing a three-dimensional closed network without periodic boundaries by embedding the system onto the surface of a sphere in four dimensions. This method can also be used to construct finite-sized gel particles for simulating the swelling of particles in a surrounding solvent. The method is described in algorithmic detail to allow the incorporation of the method into different types of simulation programs. We also present the results of Brownian dynamics simulations, analyzing the end-to-end distribution, radial distribution function, and the pore size distribution for different volume fractions and for chains with varying stiffness.