  The algebraic cluster model is is applied to study cluster states in the
nuclei 12C and 16O. The observed level sequences can be understood in terms of
the underlying discrete symmetry that characterizes the geometrical
configuration of the alpha-particles, i.e. an equilateral triangle for 12C, and
a regular tetrahedron for 16O. The structure of rotational bands provides a
fingerprint of the underlying geometrical configuration of alpha-particles.
