Locally regular coloured graphs (Q1184574)

The author introduces the concept of locally regular coloured graph as a generalization to any dimension of the concept of regularity for maps on surfaces used by \textit{W. Threlfall} [Abh. math.-phys. Kl. sächs. Akad. Wiss. 41, No. 6, 1-59 (1932; Zbl 0004.02202)]. He proves that locally regular coloured graphs can be obtained from the classical spherical, Euclidean and hyperbolic tessellations. He also describes locally regular coloured graphs on the spherical 3-manifolds.