Combinatorial properties of karyon tilings \(\mathcal{T}\) of torus \({\mathbb{T}}^{d}\) of arbitrary dimension d are studied. The main results are the following: 1) the karyon corona Cr contains all types of polyhedral stars of \(\mathcal{T}\), 2) the number of all faces of dimension a of \(\mathcal{T}\) is equal to md!/((d − a)!a!), where m is the order of \(\mathcal{T}.\)
