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## 'Platonic Planet' printed from http://nrich.maths.org/

Glarsynost the alien lives on a platonic planet whose shape is that
of a perfect regular dodecahedron.

Every day, she likes to go for a walk to have a look at her planet
and see if she has any visitors.

What fraction of the planet's surface can she see from the middle
of a face? From an edge? From a vertex?

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.