Building some Platonic Solids to take home at the Curious Minds Club (St Thomas of Canterbury Primary School, 7 February 2020)

This week at the Curious Minds Club the children built models of the Platonic Solids to take home. In the previous two weeks I had given the children Polydron Frameworks and what I call a generic version of Geomag to make the Platonic Solids. These materials are expensive and I took them home at the end of the sessions. I wanted to give the children an opportunity to make models they could take home with them.

The materials I used were simple: plastic drinking straws and pipe cleaners. (I did ponder the ethics of plastic straws, as they are due to be banned in the UK in 2020; my conclusion was that I should use up the ones that currently exist before switching to paper). Feel free to contact me for details of the construction method. Once I showed the children how to build the models they took to it quickly. They enjoyed commenting on what the models looked like as they went along. When they were building a cube: “it looks like a laptop” and “I have made a table”.

Here are all five Platonic Solids that I made. (The session overran and there was no time to take photos of the children’s models). I think they look good in black. See how the pipe cleaners form the vertex:

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Here is each one by itself:

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They all look good …. until you get to the Dodecahedron above. This was a real struggle. My first attempt is below. The edge length is 75mm, the same as the others. It was hard to make every face look like a regular pentagon.

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I thought I would try making each edge half the length (75mm to 37mm) to see if this was easier. This is how it looked during construction:

The end result is below. It was the best I could manage. I manipulated a lot of the vertices by switching the pipe cleaners around. It goes concave in places but the whole thing should be convex.

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My conclusion is that drinking straws and pipe cleaners are a cheap and easy building material for building the Platonic Solids, if you can tolerate an imperfect Dodecahedron.

I also made a whole set using neon straws, but I don’t think they look as good as the black. You can see some gaps between the pipe cleaners inside the straws.

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Borromean rings and Brunnian links at the Curious Minds Club (St Thomas of Canterbury Primary School, 6 December 2019)

This week at the Curious Minds Club we explored Borromean and Brunnian links.  We started with the Borromean rings as they are the simplest Brunnian link. I showed the children how to turn coloured pipe cleaners into circles. They made a red one and a white one, then placed the white on top of the red one and threaded a blue one through, in an over-under-over-under sequence. I showed the children that as a ring of three this is a strong link, but if you remove any one ring the whole thing falls apart.

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I asked the children to turn their flat ring into a three-dimensional structure, almost like a gryoscope.

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A drew a table to show that each ring is outside one ring and inside another ring.

Outside Inside
White Red Blue
Blue White Red
Red Blue White

I surprised the children by asking them how their Borromean ring is like the game ‘Rock, Paper, Scissors’. One girl was able to identify that each component has a different relationship with the other two components. I drew the table below and pointed out that white occupies the same positions in the table as rock; that blue corresponds to paper; and that red corresponds to scissors. I explained that the concept of ‘beating’ equates to being ‘outside’ and the concept of ‘losing to’ equates to being ‘inside’.

Beats Loses to
Rock Scissors Paper
Paper Rock Scissors
Scissors Paper Rock

By this point some of the children had discovered that they could turn their Borromean ring inside out. I encouraged all the children to practice turning their ring inside out and back again. I think this is one of the most fascinating aspects of the Borromean ring and is due to the fact that no two of the three rings are actually linked with each other.

We then moved on to making a Borromean ring of a Borromean ring! Yes, we went fractal! I asked the children to take three pipe cleaners of one colour, three of a second colour and three of a third colour. They made normal Borromean rings with their first and second colours and placed one on top of the other. They made another Borromean ring with their third colour to get the twists in the right place, undid the ends, threaded it through and retied the ends. When made three dimensional this is a very interesting object to look at.

Some children had raced a bit ahead, so I asked them to make triangles instead of circles and thread them into a ring. I showed them one I had made earlier. Two children thought the circles made a better three dimensional shape, but one boy argued in favour of his triangles. He had indeed succeeded in making something harmonious to look at.

The final task was a make a 4 component Brunnian link, with four different coloured pipe cleaners. This is trickier than the Borromean rings as the green link has to be made much smaller, but the threading is not too complicated. With a little assistance the children were able to complete theirs. I asked what would happen if one link was removed. Due to the effort involved in making it some of the children were reluctant to try this on theirs! I let them use my demo instead, and they were surprised to see the whole thing fall apart. I explained that as this happens with the Borromean rings we should expect it with the Brunnian link as they are part of the same class of links.

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Here are some photos of the children’s work.

Year 2 girl:

 

 

Year 4 girl:

Y4girl Borromean

Year 5 boy:

Y5boy Borromean

Year 6 boy:

Y6boy Borromean

Year 6 girl:

Y6girl Borromean