  We present PolarStar, a novel family of diameter-3 network topologies derived
from the star product of low-diameter factor graphs. PolarStar gives the
largest known diameter-3 network topologies for almost all radixes, thus
providing the best known scalable diameter-$3$ network. Compared to current
state-of-the-art diameter-$3$ networks, PolarStar achieves $1.3\times$
geometric mean increase in scale over Bundlefly, $1.9\times$ over Dragonfly,
and $6.7\times$ over {3-D} HyperX. PolarStar has many other desirable
properties, including a modular layout, large bisection, high resilience to
link failures and a large number of feasible configurations for every radix. We
give a detailed evaluation with simulations of synthetic and real-world traffic
patterns and show that PolarStar exhibits comparable or better performance than
current diameter-3 networks.
