Copyright © University of Cambridge. All rights reserved.

## 'Magnetic Personality' printed from http://nrich.maths.org/

I found this construction kit in a local supermarket - it cost me
less than £2 and has 60 pieces - 35 sticks and 25 metal
spheres.

The sticks are magnetic so that you can construct models by joining
them with the metal spheres (more shortly).

I started to experiment and the first question I asked myself was
whether I could make each of the platonic solids. How many sticks
and spheres I would need for each one? That is for:

- A tetrahedron
- A cube
- An octohedron
- An icosahedron
- A dodecahedron

I must admit that trying to construct the last two proved to be a
bit of a challenge but here is a picture of a cube and a
tetrahedron for you to see what I mean.

This led me to think about how many of the skeleton platonic solids
I could make in one go with the pieces available. So here is a cube
and a tetrahedron. Would I be able to make an octahedron as well
without running out of pieces? This felt highly likely but you
might want to check.

But what combinations of solids are possible? For example could I
make an icosahedron and a cube and an octahedron or would I run out
of pieces?

All this led me on to the two final challenges I am going to pose
for you:

Firstly, how many of each of the polyhedra could I make with the
set? In the picture I have several tetrahedra - how many could I
make altogether with my 60 pieces? How about cubes, octahedra and
so on?

And finally, could I choose a selection of polyhedra that used all
the pieces, if not what is the best I could do?