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?
Can you work out the dimensions of the three cubes?
Sliced
Age 14 to 16 Challenge Level:
An irregular tetrahedron has two opposite sides the same length
($a$ say) and the line joining their midpoints is perpendicular to
these two edges and is of length $b$. What is the volume of the
tetrahedron?