  A 2-nearly Platonic graph of type (k|d) is a k-regular planar graph with f
faces, f-2 of which are of degree d and the remaining two are of degrees
m_1;m_2, both different from d. Such a graph is called balanced if m_1=m_2. We
show that all 2-nearly Platonic graphs are necessarily balanced. This proves a
recent conjecture by Keith, Froncek, and Kreher.
