If you pick any two vertices of a tetrahedron with sides 10cm long, they will always be 10cm apart, because there will always be an edge that joins them. But what are the different possible distances between two vertices of a cube with sides 10cm long?

What about the different possible distances between two vertices of an octahedron with sides 10cm long?

See if you can calculate these distances exactly!

If you want a bigger challenge, try this problem on a dodecahedron…