Follow instructions to fold sheets of A4 paper into pentagons
and assemble them to form a dodecahedron. Calculate the error in
the angle of the not perfectly regular pentagons you make. Her
walk needs to start and end at the same place, and she needs to
be able to see every part of the planet's surface at some stage
during her walk. Investigate the possible paths she could take.
The challenge is to find the shortest path you can! One way of
investigating and recording this could be to create a net of a
dodecahedron, and draw the path on the net, being careful to
consider which faces will join when the net is folded up. Here
are two nets you could use, but you may find it easier to
visualise an efficient path using a different one.