  In 1992, Godsil and Hensel published a ground-breaking study of
distance-regular antipodal covers of the complete graph that, among other
things, introduced an important connection with equi-isoclinic subspaces. This
connection seems to have been overlooked, as many of its immediate consequences
have never been detailed in the literature. To correct this situation, we first
describe how Godsil and Hensel's machine uses representation theory to
construct equi-isoclinic tight fusion frames. Applying this machine to Mathon's
construction produces $q+1$ planes in $\mathbb{R}^{q+1}$ for any even prime
power $q>2$. Despite being an application of the 30-year-old Godsil-Hensel
result, infinitely many of these parameters have never been enunciated in the
literature. Following ideas from Et-Taoui, we then investigate a fruitful
interplay with complex symmetric conference matrices.
