We show that the second-order phase transition between spherical and deformed shapes of atomic nuclei is an isolated point following from the Landau theory of phase transitions. This point can occur only at the junction of two or more first-order phase transitions which explains why it is associated with one special type of structure and requires the recently proposed first-order phase transition between prolate and oblate nuclear shapes. Finally, we suggest the first empirical example of a nucleus located at the isolated triple-point.