  We conduct a numerical study of the dynamical behavior of a system of
three-dimensional crosses, particles that consist of three mutually
perpendicular line segments rigidly joined at their midpoints. In an earlier
study [W. van Ketel et al., Phys. Rev. Lett. 94, 135703 (2005)] we showed that
this model has the structural properties of an ideal gas, yet the dynamical
properties of a strong glass former. In the present paper we report an
extensive study of the dynamical heterogeneities that appear in this system in
the regime where glassy behavior sets in. On the one hand, we find that the
propensity of a particle to diffuse is determined by the structure of its local
environment. The local density around mobile particles is significantly less
than the average density, but there is little clustering of mobile particles,
and the clusters observed tend to be small. On the other hand, dynamical
susceptibility results indicate that a large dynamical length scale develops
even at moderate densities. This suggests that propensity and other mobility
measures are an incomplete measure of dynamical length scales in this system.
