Coloured knots and coloured graphs representing 3-fold simple coverings of %plane1D;54A;3 Original Research Article

It is well-known that every closed orientable 3-manifold M3 is the 3-fold simple covering M3 (K, ω) of %plane1D;54A;3 branched over a knot K: hence, M3 may be visualized by the associated coloured knot (K, ω). On the other hand. PL-manifolds of arbitrary dimension may be represented by coloured graphs, via pseudosimplical triangulations. The present paper produces an algorithm to construct a 4-coloured graph representing M3 (K, ω), directly ‘drawn over’ the coloured knot (K, ω).