Follow these easy instructions to create your very own Flexagon Christmas Card.  Your card will have four faces – two which can be seen and another couple which are hidden away. It is simple to switch between the faces and surprise your friends and family with the symmetry of your amazing Flexagon Christmas Card. It is the perfect choice for anyone who loves maths, as flexagons have been a source of mathematical fascination since the early 20th Century.

### Step 1

Get an A4 sheet of paper or card. Fold it in half and half again.

Tip: Using paper will produce a flimsy Flexagon Christmas Card, but it is great to practise with!

### Step 2

Now fold it accurately into thirds the other way. The easiest way to do this is to mark 7cm and 14cm up the shorter sides of your paper, as the short edge of your A4 paper is 21cm long.

With every fold make sure that you crease it both ways, so your paper or card is nice and flexible.

### Step 3

Number lightly in pencil on the front of your paper as follows. (We made the numbers big so you can see them!) You only need these numbers to help you know what you are doing. You won’t need them once you are experienced at making Flexagon Christmas Cards.

### Step 4

Turn over your card (left to right) and number lightly in pencil on the back of your card as follows. (The top row in step 4 is directly behind the top row in step 3.)

### Step 5

Cut a flap as follows using the central two rectangles. Make sure it is still attached on the left.

### Step 6

Fold this flap behind the number three square on the left.

### Step 7

Fold the right-hand part of your card behind, so that you can now see a column of ‘twos’.

### Step 8

Fold the flap on the left with a three on it over the front. Fold the column of twos on the right-hand side underneath. You should now just see six rectangles, each containing a number ‘one’.

### Step 9

Use a small piece of tape to secure your card.

### Step 10: Decorate your Christmas Card.

Now you have made your Flexagon Christmas Card you can decorate the four faces. Make sure you don’t block any of the folds when you do this. Here is an example we made using stronger card.

### How to reveal your hidden Flexagon Christmas Card Faces.

Fold your card in half vertically, then open it out from the other edge. Can you find all four faces?

Top Tip: If you are sending your card in the post, you might want to send an explanation so that your friend knows that this is no ordinary Christmas Card – it is a Mathematical Flexagon Christmas Card! You should also flex your card a large number of times before you send it as it will work better and better, the more times you use it!

It is thought that Flexagons were discovered by mathematician Arthur H. Stone in 1939, but it was recreational mathematician Martin Gardner who launched them to fame in the 1950s. The HexaFlexagon is the best known of all the Flexagons.