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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?

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.

A Mean Tetrahedron

Can you number the vertices, edges and faces of a tetrahedron so that the number on each edge is the mean of the numbers on the adjacent vertices and the mean of the numbers on the adjacent faces?

Lighting up Time

Age 7 to 14
Challenge Level

This lampshade was photographed in Rimini in Italy. In Africa candle holders exactly like this are often made from wire.

Lampsahde
  • Do you know the mathematical name for this shape?
  • Can you see lots of triangles?
  • What "type" of triangles are they and how many of them were needed to make this lampshade?
  • What other shapes can you see?
  • Could you make a polyhedron like this from card? How would you do it?

There's another image you might like to take a look at in the Notes .

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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