  The total face color polynomial is based upon the Poincar\'{e} polynomials of
a family of filtered $n$-color homologies. It counts the number of $n$-face
colorings of ribbon graphs for each positive integer $n$. As such, it may be
seen as a successor of the Penrose polynomial, which at $n=3$ counts $3$-edge
colorings (and consequently $4$-face colorings) of planar trivalent graphs. In
this paper we describe a state sum formula for the polynomial. This formula
unites two different perspectives about graph coloring: one based upon
topological quantum field theory and the other on diagrammatic tensors.
