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### Number and algebra

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### For younger learners

# Dodecawhat

### 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

### Key Questions

### Support

### Extension

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Age 14 to 16

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

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.

- 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?

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.

The A4 paper part of theproblem.

We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.

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?