# Blog

## Rhombic dodecahedron

By

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This decoration and the size of A4 paper share an interesting property. Get hands on to find out more!

### You will need

• A4 sheet of light card
• Pen
• Scissors
• Ruler
• Sticky tape

### What to do

#### Making the pieces

1. Measure down the long sides of the sheet of card, and make marks at 50, 149 and 248 mm on each side.

2. Measure along the short sides of the sheet of card, and make marks at 35, 105 and 175 mm on each side.
3. Look at the bottom and left sides of your page. Take your ruler, and draw a line connecting the leftmost mark to the bottom mark.
4. Now connect the middle mark to the middle mark, and finally the top mark to the right mark.
5. Look at the bottom and right sides. Connect the rightmost mark to the bottom mark, the middle mark to the middle mark and the top mark to the left mark.
6. Repeat this pattern around the top left and top right corners. Every line will be parallel to the lines in steps 3 to 5.

7. Your card will be divided into 13 diamonds and some triangles. Cut out all the diamonds – you will need 12 of them to complete this activity.

#### Joining the pieces

1. Make sure all 12 diamonds are exactly the same. Each diamond has two blunt angles and two pointy ones.
2. Take two diamonds, and put them next to each other so they share a side. Make sure the blunt angles meet at the same point. Use sticky tape to hold them together.
3. A third diamond needs to meet at the blunt angle.

Take a diamond, and tape it to the first diamond, then the second, so the blunt angles on each diamond all meet at one point. The model will no longer lay flat.

4. Find a place where two pointy angles meet. Two more pointy angles need to meet there. Tape the additional diamonds in place.
5. Keep looking around your model. Wherever pointy angles meet, you need four diamonds to meet. Wherever blunt angles meet, you need three diamonds to meet. Eventually, the shape will bend around and make a ball!

### What’s happening?

Solid shapes are much more complicated than flat shapes. Some people may recognise a regular dodecahedron, a 12-faced solid with pentagon sides. The rhombic dodecahedron also has 12 faces, but they are rhombuses (diamonds) rather than pentagons.

This activity uses a property of A4 paper. To make a rhombic dodecahedron, the diamonds need a particular ratio between their length and width, and A4 paper shares those proportions.