In recent years, there has been a growing recognition that higher-order structures are important features in real-world networks. A particular class of structures that has gained prominence is known as a simplicial complex. Despite their application to complex processes such as social contagion and novel measures of centrality, not much is currently understood about the distributional properties of these complexes in communication networks. Furthermore, it is also an open question as to whether an established growth model, such as scale-free network growth with triad formation, is sophisticated enough to capture the distributional properties of simplicial complexes. In this paper, we use empirical data on five real-world communication networks to propose a functional form for the distributions of two important simplicial complex structures. We also show that, while the scale-free network growth model with triad formation captures the form of these distributions in networks evolved using the model, the best-fit parameters are significantly different between the real network and its simulated equivalent. An auxiliary contribution is an empirical profile of the two simplicial complexes in these five real-world networks.