Document Type

Article - preprint


Mathematics (Pomona), Mathematics (CMC)

Publication Date



Lattice, Equiangular lines, Tight frame, Conference matrix


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.


Final published version can be found at: Böttcher, A., Fukshansky, L., Garcia, S.R., Maharaj, H., Needell, D., Lattices from tight equiangular frames, Lin. Alg. Appl. 510 (2016), 395-420.

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© 2016 Elsevier Inc.

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