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How to make: Christmas Special

Making gingerbread Platonic solids, Fröbel stars and Christmas flexagons

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It’s December and no longer too early to start planning for Christmas! If you’re not quite feeling Christmassy yet, this special Christmas edition of How to Make should help you get in the mood by making something delicious, mathematical or festive (or all three!).

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How to Make… Christmas flexagons

Edit: If you are a teacher and want to make Christmas flexagons will a class, you may find Rhiannon Bedford‘s slides helpful. You can download them (and a copy of our template) from TES here.

Flexagons were discovered in 1939 by Arthur H. Stone, a British mathematician studying at Princeton. 76 years later, they are still lots of fun!

You will need


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Instructions

First, colour in and cut out the template.

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Fold and glue the template in half lengthways.

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Fold along the red lines.

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Turn over and fold along the red line.

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Tuck the plain white triangle under. The two plain triangles should now be touching. Glue them together.

You have made a Christmas flexagon! Now flex it until Christmas is over…

You can read more about flexagons in Martin Gardner’s famous article.

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How to Make… Fröbel stars

Fröbel stars were invented by the 19th century educator Friedrich Fröbel. They look really nice hanging from the branches of Christmas trees.

You will need

  • Four strips of paper (quilling paper is perfect)
  • Scissors

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Instructions

Fold all four strips in half.
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Put the green strip over the purple strip.
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Put the red strip over the green strip.
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Put the orange strip over the red strip and through the purple strip.
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Pull the strips together.
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Fold the top strip of each pair over the central square, tucking the last strip through the one under it.
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Fold the red strip underneath itself so that it is next to the green strip.
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Fold the red strip over itself so that it is next to the lower red strip.
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Fold the red strip over so that the two small triangles you have made are on top of each other.
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Tuck the red strip under the green strip.
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Repeat the last 4 steps with each of the upper strips then turn it over.
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Repeat the four steps above to make points with the other four strips.
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Fold the strips over 90° anticlockwise.
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Pick the purple strip up and feed it through and out of the yellow point.
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Repeat this to make a point of each colour.
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Cut off the excess strip coming out of the point.
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Turn the star over and make four points on the other side.
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You have made a Fröbel star.
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How to Make… gingerbread Platonic solids

Tube maps are not the only material that it is fun to make Platonic solids from.

You will need

  • 12oz plain flour
  • 2 tsp ground ginger
  • 1 tsp allspice
  • $\frac{1}{2}$ tsp bicarbonate of soda
  • 4oz golden syrup
  • 1oz butter
  • 1oz soft brown sugar
  • 1 egg
  • 2 tbsp milk

Instructions

Measure all the ingredients into a mixing bowl.
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Mix all the ingredients until the mixture forms a dough. Put the ball of dough on a floured surface.
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Use a rolling pin to roll the mixture out then cut out some triangles. Use a drinking straw to poke holes in the corners of the gingerbread.
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Bake the shapes at 180°C for 12-15 minutes. Once the shapes are cooled, use ribbon to attach them into tetrahedrons.
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Alternatively, use a different number of triangles or a different shaped face and make another platonic solid of your choice.

Matthew Scroggs is a PhD student at UCL working on finite and boundary element methods. His website, mscroggs.co.uk, is full of maths and now features a video of him completing a level of Pac-Man optimally.
Twitter  @mscroggs    Website  mscroggs.co.uk    + More articles by Matthew

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