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 polygon	Number of colours	Link
Square	2	link
Square	4	link
Square	5	link
Square	9	link
Square	10	link
Square	13	link
Square	16	link
Hexagon	3	link
Hexagon	4	link
Hexagon	7	link
Hexagon	9	link
Hexagon	12	link
Hexagon	13	link
Triangle	2	link
Triangle	4	link
Triangle	14	link
Triangle	18	link
Triangle	24	link
Triangle	26	link

NB. The colours are chosen at random. Examples using only one colour are not included!

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