# Blog

## Lolly-toothpick platonic solids

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There are five regular solids – we call these the Platonic solids. The faces of a platonic solid are all the same, regular shape, and the same number of faces meet at each vertex (corner). In this activity you can make all five of them!

Safety: Use clean hands and equipment if you plan to eat the lollies later.

### You will need

• Lots of toothpicks
• Jelly snakes or similar jelly lollies, cut into small pieces, about 5-10 mm wide.

### To make a tetrahedron

1. Take three toothpicks and arrange them into a triangle.
2. At each corner, push the two toothpicks into a piece of jelly lolly.
3. Take three more toothpicks, and push one into each corner of the triangle, so the other ends all meet at a point. Use a piece of lolly to hold these ends together.
4. You will now have a triangle-based pyramid, also known as a tetrahedron!

### To make a cube

1. Take four toothpicks and four pieces of lolly. Make a square out of the toothpicks, holding the ends together with the pieces of lolly.
2. Take four more toothpicks, sticking one into each corner vertically.
3. Put a piece of lolly on top of each vertical toothpick.
4. Take four more toothpicks and connect the four new pieces of lolly into a square.
5. You will now have a cube! It’s not a rigid shape, so it might sag a bit.

### To make an octahedron

1. Take a piece of lolly and stick four toothpicks into it, to make a cross shape.
2. Take four pieces of lolly and put one on to each of the ends of the cross.
3. Take four toothpicks, and stick them into the lollies at the end of the cross to make a square. At this point your shape will not lie flat any more.
4. Take four more toothpicks, and push one into each corner of the square, so the other ends all meet at a point. Use a piece of lolly to hold these ends together.
5. You now have an octahedron! It looks a bit like a crystal.

### To make an icosahedron

The icosahedron and dodecahedron are quite difficult to explain. These instructions will give you a start, but you’ll have to work out how to finish these shapes yourself!

1. Take a piece of lolly and stick five toothpicks into it, to make a sort of star (*) shape.
2. Take five pieces of lolly and put one on to each of the ends of the star.
3. Take five toothpicks, and stick them into the lollies at the end of the star to make a pentagon. At this point your shape will not lie flat any more.
4. You now have one vertex (corner) surrounded by five triangles. Every vertex of the icosahedron needs to look like this one. That means that every vertex must have five toothpicks coming from it, and every face must be a triangle.
5. The completed icosahedron has 12 vertices (lolly) and 30 edges (toothpicks). So far, you’ve used 6 lollies and 10 toothpicks.

### To make a dodecahedron

1. Make a pentagon using 5 lolly pieces and 5 toothpicks.
2. Get 5 more toothpicks and stick one into each corner of the pentagon to make ‘legs’. Then put a piece of lolly on the other end of each of those toothpicks.
3. Take two toothpicks and join them with a piece of lolly. Use the two connected toothpicks to join two adjacent ‘legs’ and make a pentagon. Repeat this with each pair of adjacent ‘legs’ to make a ring of 5 pentagons surrounding the original pentagon.
4. The dodecahedron has 12 pentagon faces. At each vertex, three edges meet. The completed shape will use 20 pieces of lolly and 30 toothpicks.
5. When you finish your dodecahedron, it will probably sag a lot. To make a pentagon more rigid, you can stick 5 toothpicks into a piece of lolly, and then stick the other ends of the toothpicks into each of the corners of the pentagon. If you do this to all the pentagons, you’ll get a big, round shape made of triangles.

Good luck!

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## 3 responses

1. Glenn Westmore

The Platonic solids are comprised of the same regular polygon. The Greeks believed that they underpinned the structure of the five elements.

2. Mark

3. David

Oh dear!

I can’t find it on Glenn’s site, sadly.

I found another article about Plato’s philosophical musings on the nature of solids:
https://www.mathpages.com/home/kmath096/kmath096.htm

It’s a bit heavy going, but there’s some interesting stuff if you’re into the history of mathematics.

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