Crystals cannot have five-fold symmetry
The old claim turned out to be wrong and was rejected by evidence.
TaughtA crystal is a periodic repeating lattice. Five-fold rotational symmetry is geometrically impossible in a crystal: you cannot tile a plane with pentagons.
NowQuasicrystals have ordered but non-repeating structures with forbidden symmetries. Dan Shechtman observed one in 1982, was ridiculed for years, and won the 2011 Nobel Prize in Chemistry.
What actually happened
Shechtman's electron diffraction pattern in April 1982 showed ten bright points in a ring: a symmetry that crystallography said could not exist. His lab notebook entry for that day reads, in Hebrew, "10 Fold???"
The reception was brutal. He was asked to leave his research group, told to reread the textbook, and Linus Pauling, twice a Nobel laureate, said publicly that there are no quasicrystals, only quasi-scientists. Shechtman was vindicated as more quasicrystals were found and the mathematics caught up, aided by Roger Penrose's aperiodic tilings, which fill a plane with five-fold symmetry using shapes that never repeat exactly. In 1992 the International Union of Crystallography rewrote the definition of "crystal" to mean any solid with a discrete diffraction pattern, dropping the requirement of periodicity, which is the moment the textbook officially changed. A naturally occurring quasicrystal was found in a Russian meteorite in 2009.
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Who was taught this
Still standard through 1995, so anyone who finished school between 1950 and 1992 learned the earlier version.