  A vertex colouring of some graph is called perfect if each vertex of colour
$i$ has the same number $a_{ij}$ of neighbours of colour $j$. Here we determine
all perfect colourings of the edge graphs of the hypercube in dimensions 4 and
5 by two and three colours, respectively. For comparison we list all perfect
colourings of the edge graphs of the simplex in dimensions 4 and 5,
respectively.
