# Numer of (distinct?) $d$ dimensional irreducible representations

I found a footnote on page 140 of this book that reads:

For a general $$d$$-dimensional quasicrystal, there is more than one $$d$$-dimensional irreducible representation. For the case of two-dimensional pentagonal symmetry, which describes the original Penrose tilings, there are two distinct two-dimensional representations of the pentagonal group.

From which my take-home message is: for regular crystals in $$d$$ dimensions, there is only one $$d$$ dimensional irreducible representation.

But then why does the dihedral group of order $$n$$ (even, for instance) have $$(n-2)/2$$ two-dimensional irreducible representations, as listed here?