A brief account of the algebraic cluster model (ACM) is given. Applications to cluster structures composed of k α-particles with k = 2 (Z2 symmetry), k = 3 (D3h symmetry) and k = 4 (Td symmetry) are presented. Experimental evidence for the occurrence of these symmetries in 8Be (Z2), 12C (D3h), and 16O (Td) is shown.
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