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Platonic Planet

Glarsynost lives on a planet whose shape is that of a perfect regular dodecahedron. Can you describe the shortest journey she can make to ensure that she will see every part of the planet?

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Tet-trouble

Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?

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Cubic Conundrum

Which of the following cubes can be made from these nets?

Cubic Net

Age 14 to 18 Challenge Level:

It is important to try to visualise the net wrapped up into a cube, using the following ideas
  1. You might like to think of the yellow and purple faces as the 'Top' and 'Bottom' of the 3D cube.
  2. The Blue - White - Red - Green faces wrap around to make the sides of the cube
  3. Twisiting the 'Top' of the cube will cause the top layer of the Blue - White - Red and Green faces to twist -- Why not try this out
  4. Twisting the 'Bottom' of the cube will cause the bottom layer of the Blue - White - Red and Green faces to twise -- Why not try this out?
You might also like to try to investigate the net whilst holding a 3D cube.