  The dynamically triangulated random surface (DTRS) approach to Euclidean
quantum gravity in two dimensions is considered for the case of the elemental
building blocks being quadrangles instead of the usually used triangles. The
well-known algorithmic tools for treating dynamical triangulations in a Monte
Carlo simulation are adapted to the problem of these dynamical
quadrangulations. The thus defined ensemble of 4-valent graphs is appropriate
for coupling to it the 6- and 8-vertex models of statistical mechanics. Using a
series of extensive Monte Carlo simulations and accompanying finite-size
scaling analyses, we investigate the critical behaviour of the 6-vertex F model
coupled to the ensemble of dynamical quadrangulations and determine the matter
related as well as the graph related critical exponents of the model.
