  This paper supplies additions to our paper in Linear Algebra Appl. 510 (2016)
395--420 on integral spans of tight frames in Euclidean spaces. In that
previous paper, we considered the case of an equiangular tight frame (ETF),
proving that if its integral span is a lattice then the frame must be rational,
but overlooking a simple argument in the reverse direction. Thus our first
result here is that the integral span of an ETF is a lattice if and only if the
frame is rational. Further, we discuss conditions under which such lattices are
eutactic and perfect and, consequently, are local maxima of the packing density
function in the dimension of their span. In particular, the unit (276, 23)
equiangular tight frame is shown to be eutactic and perfect. More general tight
frames and their norm-forms are considered as well, and definitive results are
obtained in dimensions two and three.
