Special Collection: Perfect colourings

There are 19 entries in this table of all the perfect colourings in this collection.
This property is considered for the plane filled with either squares, hexagons or equilateral triangles. A perfect colouring is a colouring of the basic polygons such that any symmetry operation permutes the colours of the polygons.
As an example, consider the checkerboard coloring of the square lattice. A rotation about the centre of any square leaves the colours unchanged, while moving one square to the left interchanges the two colours. Hence the cherboard is a perfect colouring of just two colours.
The first entry in the table is the basic polygon, the second entry the number of colours and the last entry the link to the pattern.
Basic polygonNumber of coloursLink
Square2link
Square4link
Square5link
Square9link
Square10link
Square13link
Square16link
Hexagon3link
Hexagon4link
Hexagon7link
Hexagon9link
Hexagon12link
Hexagon13link
Triangle2link
Triangle4link
Triangle14link
Triangle18link
Triangle24link
Triangle26link
NB. The colours are chosen at random. Examples using only one colour are not included!

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