The Dodecahedron


Why do this problem?

It provides an exercise in trigonometry using angles of 72, 36 and 54 degrees.

Key questions

How do you find the shortest distance between two points on the net?

Does the distance on the surface change when the flat net is folded into the shape of the dodecahedron?

Can you usesymmetry?

Can you work out any angles in the diagram?

Possible extension

Find the shortest distance through the centre of the dodecahedron. See this student's solution.