  One-dimensional (1D) quasicrystals exhibit physical phenomena associated with
the 2D integer quantum Hall effect. Here, we transcend dimensions and show that
a previously inaccessible phase of matter --- the 4D integer quantum Hall
effect --- can be incorporated in a 2D quasicrystal. Correspondingly, our 2D
model has a quantized charge-pump accommodated by an elaborate edge phenomena
with protected level crossings. We propose experiments to observe these 4D
phenomena, and generalize our results to a plethora of topologically equivalent
quasicrystals. Thus, 2D quasicrystals may pave the way to the experimental
study of 4D physics.
