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?

Tet-trouble

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

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.