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Round cubic decoration

By David Shaw, 1 July 2014

Cones are kinda round, but put them together right and you can make a cubic decoration. Sound confusing? Don’t worry, it’s really simple and really fun!

You will need

What you will need.

• A copy of the printout
• Scissors
• Sticky tape
• Glue stick

If you don’t have a printer, you can make your own template. Draw six equal circles, and then measure an angle of 255 degrees at the middle of each, to make a ‘Pac-Man’ shape.

What to do

1. Cut out the six segments.
   

   Hold each cone together with sticky tape.

2. Bend one segment so the two straight sides meet and it becomes a cone. Hold it together with a piece of sticky tape.
3. Repeat with the other segments to make six cones.
4. Put one cone circle-side down on a table.
5. Put glue on the outside of a second cone, and lay it on the first so the circle faces forward and the apexes (points) of the two cones touch.
6. Glue the outside of a third cone and place it so it touches the other two and the circle faces left. Glue and place two more cones so the circles face back and right. The apexes of all the cones should meet in the same spot.
7. Put glue on the last cone and turn it upside down so the apex is on the bottom. Stick it on top of the other cones.
   

   Glue the cones so the apexes touch.

8. Wait for the glue to dry, and then look at your construction. It is round, but it has six ‘faces’, similar to a cube.

For an extra challenge, you can make a dodecahedral decoration with 12 cones. Download the template here.

What’s happening?

The shape you’ve made looks round when you look at it one way, but from another angle it looks square. There are six circular ‘faces’ appearing at the top, bottom, front, back, left and right. This is the same arrangement as the faces of a cube. It’s like a hidden structure to our not-quite-round decoration!

The completed decoration.

Scientists and mathematicians are very good at finding hidden structures inside objects. One way to find hidden cubes is to look for symmetry. Symmetry comes in different forms – you can turn a cube upside down, and it will look the same. You can rotate it 90 degrees, or look at it in a mirror and it will look the same.

There are hidden symmetries inside all crystals. Scientists use a technique called X-ray crystallography to examine these symmetries and discover the hidden shapes inside crystals.

More information

Another mathematical bauble for you to make!

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