Face Painting
Here is a picture of the five Platonic solids:
Imagine you want to make each of the five Platonic solids and colour the faces so that, in every case, no two faces which meet along an edge have the same colour.
Can you find the least number of colours for which this is possible for each polyhedron.
How did you go about finding your solutions?
If you'd like to make these solids out of paper, have a look at Ian Short's article.
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Tetrahedron Faces
One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?
Redblue
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?
Dodecamagic
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?