In 2000, Rees and Shalaby constructed simple indecomposable two-fold cyclic triplesystems for all v ≡ 0, 1, 3, 4, 7, and 9 (mod 12) where v = 4 or v ≥ 12, using Skolem-type sequences.We construct, using Skolem-type sequences, three-fold triple systems having theproperties of being cyclic, simple, and indecomposable for all admissible orders v, withsome possible exception...