Colorful dodecahedron

Geometry Level 3

This is a dodecahedron:

Let's suppose all sides are painted either $\color{#D61F06} \text{red}$ , $\color{#20A900} \text{green}$ or $\color{#3D99F6} \text{blue}$ .

And at one vertex they meet like this:

Is it possible that the other faces could be painted such that at no vertex they meet like this?

Yes No

1 solution

Geoff Pilling
Feb 19, 2018

Here is my attempt at an intuitive solution...

Think of the dodecahedron as a globe, with green being land and red and blue being red and blue water. If you follow the green border to the right, until you get back to the original position, you will need to eventually hit red water, which will look like the second image.

Colorful dodecahedron

1 solution

0 pending reports