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Face Painting

You want to make each of the 5 Platonic solids and colour the faces so that, in every case, no two faces which meet along an edge have the same colour.


Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?


Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

Tetrahedron Faces

Age 7 to 11 Challenge Level:
Some children from Carr head Primary School sent in this solution.  It's actually a solution to a different question being asked - they worked on not having to use each of the 4 colours for each arrangement. We have included it here as it's shows a really good piece of work. Here is what they wrote:-

I am writing to you because we think that we (9 kids from Carr Head Primary School) have found a solution for your tetrahedron question and here’s how we did it. Has anybody else found a solution yet?
First we split into 3 different groups,  Elliott, Ben B and Oliver were in one group but we started by making a 3D tetrahedron. Second we coloured them with all the colours properly, then we numbered the faces.
Next we put the first letters of the colours (B,G,Y,R) and put the numbers of the faces
1 2  3 4
Then swapped them around like 1,3,2,4 but we noticed that we were rotating it. An answer was 24 but that was wrong.
Here is the table that works. This doesn’t rotate and the answer would be 10 because you only have 1 blue all the time and it needed 4 of all the colours added up.

If you try this, then do send us what you find out.