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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?

Three Cubes

Can you work out the dimensions of the three cubes?


Age 14 to 16
Challenge Level

Image of tetrahedron with sides of length

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?