  We consider the set of all linear combinations with integer coefficients of
the vectors of a unit tight equiangular $(k,n)$ frame and are interested in the
question whether this set is a lattice, that is, a discrete additive subgroup
of the $k$-dimensional Euclidean space. We show that this is not the case if
the cosine of the angle of the frame is irrational. We also prove that the set
is a lattice for $n = k+1$ and that there are infinitely many $k$ such that a
lattice emerges for $n = 2k$. We dispose of all cases in dimensions $k$ at most
$9$. In particular, we show that a $(7,28)$ frame generates a strongly eutactic
lattice and give an alternative proof of Roland Bacher's recent observation
that this lattice is perfect.
