“…Nevertheless, we either know few about for which group, the spectral set conjecture fails. We only know that the direction ‘Spectral sets Tiles’ fails on [15], [10], when prime and and when prime and [1]; the direction ‘Tiles Spectral sets ’ fails on [12], , where is prime with gcd [4] and [5]. Actually, these non‐tile spectral sets (respectively, non‐spectral tiles) in finite abelian groups lead to non‐tile spectral sets (respectively, non‐spectral tiles) in euclidean spaces.…”