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.