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.