We investigate the equilibrium morphological properties of a symmetric
ABC triblock copolymer in the strong segregation regime. Although a t
ricontinuous double diamond phase has been experimentally reported wit
hin a large region of the phase diagram, we find that neither gyroid n
or double diamond cubic phases are stable relative to lamellae and cyl
inders in the asymptotic limit of strong segregation(SSL). However, th
is finding does not rule out stable equilibrium cubic phases at interm
ediate molecular weights or moderate temperatures. Moreover, in contra
st to the experimental conclusions, the gyroid structure is shown to b
e marginally stable with respect to the double diamond structure in th
e SSL.