A vertex colouring of some graph is called
perfect if each
vertex of colour
![$i$](img32.png)
has the same number
![$a_{ij}$](img35.png)
of neighbours of
colour
![$j$](img36.png)
. 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.