  Friezes with coefficients are maps assigning numbers to the edges and
diagonals of a regular polygon such that all Ptolemy relations for crossing
diagonals are satisfied. Among these, the classic Conway-Coxeter friezes are
the ones where all values are natural numbers and all edges have value 1. Every
subpolygon of a Conway-Coxeter frieze yields a frieze with coefficients over
the natural numbers. In this paper we give a complete arithmetic criterion for
which friezes with coefficients appear as subpolygons of Conway-Coxeter
friezes. This generalizes a result of our earlier paper with Peter Jorgensen
from triangles to subpolygons of arbitrary size.
