Ga and In crystallize in unusual open ground-state crystal structures. Rece
nt experiments have discovered that Ga under high pressure transforms into
a close-packed structure, while this has so far not been observed for In. R
esults from first principles calculations explain in a simple way this diff
erence in behavior We predict a so far undiscovered transition of In to a c
lose-packed structure at extreme pressures and show that the structure dete
rmining mechanism originates from the degree of s-p mixing of the valence o
rbitals. Group-III elements are shown to strongly disobey the standard corr
esponding-state rule.