  We describe the asymptotic properties of the edge-triangle exponential random
graph model as the natural parameters diverge along straight lines. We show
that as we continuously vary the slopes of these lines, a typical graph drawn
from this model exhibits quantized behavior, jumping from one complete
multipartite graph to another, and the jumps happen precisely at the normal
lines of a polyhedral set with infinitely many facets. As a result, we provide
a complete description of all asymptotic extremal behaviors of the model.
