  We propose and study a model with glassy behavior. The state space of the
model is given by all triangulations of a sphere with $n$ nodes, half of which
are red and half are blue. Red nodes want to have 5 neighbors while blue ones
want 7. Energies of nodes with different numbers of neighbors are supposed to
be positive. The dynamics is that of flipping the diagonal of two adjacent
triangles, with a temperature dependent probability. We show that this system
has an approach to a steady state which is exponentially slow, and show that
the stationary state is unordered. We also study the local energy landscape and
show that it has the hierarchical structure known from spin glasses. Finally,
we show that the evolution can be described as that of a rarefied gas with
spontaneous generation of particles and annihilating collisions.
