Abstract
A brief account of the algebraic cluster model (ACM) is given. Applications to cluster structures composed of k α-particles with k = 2 (Z_2 symmetry), k = 3 (D_3h symmetry) and k = 4 (T_d symmetry) are presented. Experimental evidence for the occurrence of these symmetries in ^8Be (Z_2), ^12C (D_3h), and ^16O (T_d) is shown.
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