Balanced \(3\)-nearly Platonic graphs

A balanced 3-nearly Platonic graph of type (k, d) is a kregular planar graph with three faces of the same degree m, and all f − 3 remaining faces of degree d 6= m. We present constructions of infinite families of balanced 3-nearly Platonic graph of type (k, d) for all admissible pairs (k, d), whose existence was claimed by Deza, Dutour Sikirič, and Shtogrin in 2013.