  A plane graph is l-facially k-colourable if its vertices can be coloured with
k colours such that any two distinct vertices on a facial segment of length at
most l are coloured differently. We prove that every plane graph is 3-facially
11-colourable. As a consequence, we derive that every 2-connected plane graph
with maximum face-size at most 7 is cyclically 11-colourable. These two bounds
are for one off from those that are proposed by the (3l+1)-Conjecture and the
Cyclic Conjecture.
