Materials with triangular arrangements of transition metal ions are of great interestf or their complex magnetism resulting from geometric frustration. This paper describes the stepwise formationo fk agomelattices of open shell transition-metal ions from half-delta chains to delta/sawtooth chains, and finally kagomen ets. The systemsc an be viewed as at estbedf or magnetic studies since av ariety of spin states can be introduced across the same structure type, and progress through increasing levels of structuralc omplexity and dimensionality.T he synthetica nd structural development of this continuumi ss tudied here in well-formed single crystals of A 2 M 3 (MoO 4 ) 3 (OH) 2 (A = K, Rb; M = Mn, Co), CsM 2 (MoO 4 ) 2 (OH) (M = Mn, Fe, Co, Zn), and KM 3 (MoO 4 ) 2 O(OH) (M = Mn).[a] Dr.Supporting information and the ORCID identification number(s) for the author(s) of this article can be found under: https://doi.