Pentagons, colours and permutations
Here we see 12 ways to colour a pentagon with 5 colours. Are they all the possible combinations? Indeed, the number of combinations is 24 (which corresponds to the number of permutations of 4 elements) and the image shows the 12 even permutations.
We can examine this problem in the model that represents the 5 cubes in a dodecahedron: the variously coloured pentagons appear in the 5-pointed stars that we see on the faces of the dodecahedron.
The image appeared in the survey "Officina della matematica", in the number 1 of the magazine XlaTangente.
© matematita
immagine di Gian Marco Todesco
The image belongs to the sections...:
Five cubes in a dodecahedron (3D geometry)
Number 1 (From "XlaTangente")
Further information:
http://www.toonz.com/personal/todesco
