Perfect precise colourings of \(\{3,n\}\) with \(n+1\) colours (Q1021288)

The regular tiling \(\{3,n\}\), in which \(n\) triangular tiles meet at each vertex, exists on the sphere, the Euclidean plane, or the hyperbolic plane when \(n< 6\), \(n=6\), or \(n> 6\), respectively. A colouring of such a tiling with \(n+1\) colours is called precise if no colour occurs more than once at each vertex. If every direct symmetry of the tiling permutes the colours, the colouring is called chirally perfect. In the paper the author discusses chirally perfect precise colourings of \(\{3,n\}\) with \(n+1\) colours. An algorithm for finding colour permutations at each vertex is given.