Dodecawhat
Age 14 to 16
Challenge Level 
Why do this problem?
The stimulus for the problem is the engaging context of the construction of the solid. Is this really a regular dodecahedron and how can we be sure?Possible approach
Without discussing how or why the pentagon is regular,
encourage learnersto make pentagons and put them together to make a
dodecahedron.
Then challenge them to examine whether the pentagons are
actually regular or not.
Key Questions
- How do you know this is a regular pentagon?
- What would have to be the case for the pentagon to be regular (all sides and all angles equal)?
- What do we know?
- What mathematics do you know that might be useful?
Support
Making this and other solids in similar ways, see the article
on constructing platonic solids. The focus for the learners is
on reading and following written instructions as much as on gaining
greater familiarity with 3D shapes.
Extension
The A4 paper part of theproblem.
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Glarsynost lives on a planet whose shape is that of a perfect regular dodecahedron. Can you describe the shortest journey she can make to ensure that she will see every part of the planet?
