I'm trying to diagramize some colour swatches at work, and I wanted a pattern that could be scaled up to n colours while still being symmetrical. The key is to ensure that every colour has every other colour as a neighbour.(adsbygoogle = window.adsbygoogle || []).push({});

Possible?

Here's what I mean:

2 colours: a pie cut into 2 pieces, one of each colour. Both pieces are the same shape, both are bordered by the other colour(s).

3 colours: a pie cut into 3 pieces, one of each colour. All 3 pieces are the same shape, all have every other colour as a neighbour.

4 colours: a pie cut into 4 pieces, one of each of 4 colours. But 2 pairs colours do not share a border, sinced they're kitty corner. (It is possible to do it by moving into the 3rd dimension - a tetrahedron will do nicely, but that's cheating.)

Is there a way of making a pattern (no matter how complex or convoluted) such that each colour has the same shape (tile), and each borders every other? And is in only 2-dimensions?

What is the maximum number of colours that one can accomodate?

I doubt there's anything practical that I could use at work, but now I have an academic curiosity.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Pattern possible?

Loading...

Similar Threads for Pattern possible | Date |
---|---|

Is it possible to make science as marketable as Engineering? | Nov 30, 2017 |

Can anyone solve this pattern? | Mar 23, 2016 |

Find an unusual pattern | Feb 13, 2016 |

**Physics Forums - The Fusion of Science and Community**