Further fun with the Archimedean Solids at the Curious Minds Club (St Thomas of Canterbury Primary School, 13 March 2020)

This week at the Curious Minds Club we continued to build the 13 Archimedean Solids, with Polydron Frameworks and Magformers.

My Y2 girl who got half way through a Truncated Icosahedron two weeks ago (then had to miss last week’s session) was happy to finish it. She then got her first go at Magformers. She made several of the Platonic Solids from looking at a picture of the net, then made a lovely symmetrical pattern on her own initiative.

I asked my two Y1s to build a Truncated Cube in Polydron. Once they had got the alternation correct at the start (put a triangle on one edge of the octagon, miss one edge, add another triangle etc) they were able to bring the whole solid together. They needed a little help snapping it together at the end.

My Y5 boy completed the Icosidodecahedron in Polydon, having made it in Magformers last week. My Y4 girl made the Cuboctahedron in Polydron first, then in Magformers. She built the Rhombicuboctahedron in a Polydron net really quickly, then needed quite a lot of help bringing it together. With a few minutes left at the end I gave her the Tangram puzzle. She solved it in a few minutes with no help. My Y6 girl and Y6 boy attempted the Rhombicuboctahedron in Polydron. It didn’t go quite to plan. Bob was born instead.

Here are the photos:

Y2 girl. Truncated Icosahedron (you may know it as a football); three Platonic Solids (can you name them?)

Truncated Icosahedron and Platonic Solids 13 March Y2 girl

 

Y1 girl. Truncated Cube; half an Icosidodecahedron (to be continued).

Truncated Cube and half Icosidodecahedron 13 March Y1 girl

 

Y1 boy. Truncated Cube; Truncated Octahedron; a Heart.

 

Y4 girl. Rhombicuboctahedron; Cuboctahedron; a completed Tangram.

Rhombicuboctahedron and Cuboctahedron 13 March Y4 girl

 

Y5 boy. Icosidodecahedron. Really pleased with the angle I took this at: you can really see the line of reflection symmetry.

Icosidodecahedron 13 March Y5 boy

 

Y6 girl.   Meet Bob. Apparently he doesn’t have a best side. He looks good from every side. Hard to disagree.

Bob 4 of 4 13 March Y6 girlBob 2 of 4 13 March Y6 girlBob 1 of 4 13 March Y6 girlBob 3 of 4 13 March Y6 girl

 

 

 

 

Continuing the Archimedean Solids at the Curious Minds Club (St Thomas of Canterbury Primary School, 6 March 2020)

This week at the Curious Minds Club we continued to build the 13 Archimedean Solids. We used Polydron Frameworks and a new material – Magformers.

My Y6 girl and Y6 boy sat together and used the Polydron. They started with the Truncated Dodecahedron. I then asked them to make the Cuboctahedron, explaining that it uses the six squares from the Cube and the eight triangles from the Octahedron (hence the name). Continuing with this theme, I asked them to make the Icosidodecahedron: it uses the 20 triangles from the Icosahedron and the 12 pentagons from the Dodecahedron. They needed very little help from me to work through these.

Meanwhile I introduced my Y1 girl, Y1 boy and Y5 boy to Magformers. The younger children can find it hard to snap together the Polydron pieces so I wanted to try them on a material that uses magnets to join the pieces together. I started them on all five Platonic Solids, asking them to use a picture of the net to make the shape in two dimensions, then lift it up and join the edges together. This worked really well. Even the Icosahedron comes together well, provided you work from one end to make one half, then switch to the other end, make the other half and bring them together.

My Year 1 girl was then determined to have a go at the Truncated Icosahedron in Polydron. She had seen an older girl make one last week and must have thought “I can do that”. With some reminders that every pentagon is surrounded by hexagons she was able to complete this one. She took it out to show her mum at the end and looked very proud.

I asked my Y1 boy to make a Cuboctahedron in Magformers, from a picture of its net. He cracked the net and just needed a little help lifting it up and joining the edges. He then made some fun shapes: a fish, hourglass and small star.

My Y5 boy also made the Cuboctahedron in Magformers. He then asked for ‘something harder’ so I showed him the net of the Icosidodecahedron, which he cracked. Not content with this, he went on to make a copy of the Compound of Two Tetrahedron (not an Archimedean Solid but I brought my model with me again as it is such a nice thing to look at). He worked really hard to figure out where each of the 24 triangles should go.

Here are the photos.

Y6 girl. Truncated Dodecahedron; Icosidodecahedron.

 

Y6 boy. Truncated Dodecahedron; Cuboctahedron.

 

Y1 girl. Truncated Icosahedron.

Truncated Icosahedron 6 March Y1 girl

 

Y1 boy. Cuboctahedron; Fish; Hourglass; two views of a Small Star; one of the Dodecahedrons.

 

Y5 boy. Cuboctahedron; one of the Dodecahedrons; Icosidodecahedron; Compound of Two Tetrahedra.

 

At the end of the session it is irresistible to build some towers.

 

This one gets bigger and bigger. It ended with a Tetrahedron on top, then threatened to topple over so we had to stop.

 

 

 

Starting the Archimedean Solids at the Curious Minds Club (St Thomas of Canterbury Primary School, 28 February 2020)

Before half term we built all five Platonic Solids, in various materials, so this week at the Curious Minds Club we made a start on the 13 Archimedean Solids. The material was Polydron Frameworks. I gave a brief account of who Archimedes was.

I explained that we would start by truncating all five Platonic Solids, and that truncation meant slicing off every vertex. I gave each child a piece of paper I had prepared: it had a triangle drawn in pencil, with each edge marked into thirds. I labelled the markings A,A; B,B; and C,C, gave each child a pencil and ruler and asked them to join the letters and shade through the area near the vertex. I asked them how many edges the new shape had. They counted to six and told me the new shape was a hexagon. I pointed out that we started with three edges and ended with six edges; one boy was quick to tell me this meant we had doubled the number of edges. I picked up a Tetrahedron and said we were going to truncate it: the four faces that were triangles would now be hexagons, and we would need four new triangles to replace the old vertices. I gave each child four hexagons and four triangles and put a model of a Truncated Tetrahedron on the table for them to copy if needed. Every child was able to complete this activity quite quickly: some studied the model a lot, while others just glanced at it.

We then moved on to the Truncated Octahedron. The Octahedron’s eight faces are also triangles, so these are replaced by eight hexagons. The vertices are replaced by six squares. I had a model available for those who needed it.

Two Y6 children moved ahead of the others so I started them on the Truncated Cube. I gave them a square drawn in pencil, again with each edge marked into thirds. The markings were A,A; B,B; C,C; D,D. After joining the letters they knew they had made an octagon. I reminded them that they had doubled the number of edges. I gave them six octagons and eight triangles and they happily built this solid. I was unable to make a model: I only had enough octagons in my collection for two Truncated Cubes to be made at the same time. I was able to provide a picture.

I started a Y1 girl and a Y4 girl on making their own Truncated Dodecahedron. I gave them both 12 decagons and 20 triangles. This had to be done from a picture. The Y4 girl only needed a little assistance from me. The Y1 girl needed a bit more helping snapping the Polydron pieces into place, but she had no problem working out which piece went where. At the end of the session she took it to show her dad, and he looked very impressed. I was not surprised, as this is the second biggest of the 13 Archimedean Solids.

Meanwhile a girl in Y2 made a start on the Truncated Icosahedron. She used a picture to help her, and my tip that a pentagon is surrounded just by hexagons. She ran out of time, so I promised she could finish it next week. A girl in Y6 was able to complete this solid, and looked intrigued when I pointed out that this is the shape of a football.

My Y6 boy had noticed that I had brought with me a model of a Compound of Two Tetrahedra which I was keeping to one side in case I wanted to use it. I had used yellow and red triangles to really bring out the fact that it looks like two separate tetrahedra that have been spliced together. He asked if could make his own copy of it and I was happy to agree. He needed very little help from me, and I could tell he was really proud when he had finished.

I welcomed two new boys to my club this week, brothers from Y1 and Y5. After they had completed the Truncated Tetrahedron and Truncated Octahedron I decided to take them back to the Platonic Solids as they had missed these sessions. I started them on a Cube as I knew they would have seen one before. I showed them a net and got them to build it from there. I followed this with a Tetrahedron and an Octahedron. The Y1 boy did need some help in snapping the Polydron into place, but he got stuck into the activities with enthusiasm.

Below are some photos to enjoy.

Y1 girl. Truncated Dodecahedron; Truncated Tetrahedron; she sneaked in a Cube when I wasn’t looking.

Archimedean solids 28 Feb Y1 girl

 

Year 1 boy. Truncated Tetrahedron; Cube; Octahedron.

Archimedean solids 28 Feb Y1 boy

 

Year 5 boy. Cube; Octahedron; Truncated Tetrahedron.

Archimedean solids 28 Feb Y5 boy

 

Year 2 girl. Truncated Icosahedron (to be completed next week).

Archimedean solids 28 Feb Y2 girl

 

Y6 girl. Truncated Icosahedron; Truncated Octahedron; Truncated Cube.

Archimedean solids 28 Feb Y6 girl

 

Y4 girl. Truncated Dodecahedron; Truncated Octahedron; Truncated Tetrahedron.

Archimedean solids 28 Feb Y4 girl

 

Y6 boy. Two views of the Compound of Two Tetrahedra.

Archimedean solids 28 Feb Y6 boy 3 of 4Archimedean solids 28 Feb Y6 boy 2 of 4

What a collection! A Truncated Octahedron sitting on top of: Truncated Cube; containing a Truncated Tetrahedron; containing a Cube; containing a Tetrahedron.

Archimedean solids 28 Feb Y6 boy 4 of 4

 

Building a Sierpinski tetrahedron at the Curious Minds Club (St Thomas of Canterbury Primary School, 14 February 2020)

I started this week’s session of the Curious Minds Club with some geometric snacks. First up were some nachos. I asked the children what type of triangle the nacho is. We talked about the Isosceles triangle last week, but none of them remembered. I wrote it on the whiteboard this week, to aid their learning.

Next up were some snacks I made, using cocktail sticks and midget gems:

Tetrahedron snacks

I told the children they could eat one if they could name the shape. One boy said triangle-based pyramid. I said this was correct, but that this shape has two names. I gave a hint about the first letter, and a girl very proudly said tetrahedron. I then handed one round to everybody, but made them all say tetrahedron first.

I explained that this week’s activity was to build Sierpinski’s tetrahedron, a three dimensional version of Sierpinski’s triangle. I showed them one part of it I had made using the generic version of Geomag that we used recently to build the Platonic Solids. I asked them to use just one colour to make the first part, then repeat this with a different colour. I got them to work in teams to add their four parts together to make a two layered Sierpinski tetrahedron. It involved removing some of the vertices, which the children worked out.

Two cousins (Y2 and Y4) made this (there was not enough dark blue to complete one part):

 

A boy and girl in Y6 made this:

 

For the rest of the session some children used the wooden pattern blocks to complete some more pattern boards. Others played Dotty Dinosaurs, a game about shapes. I asked two children to test a new game I have invented, with the working title of Plato’s Polyhedral Dice Game. Each child had five dice in the shape of the five Platonic Solids, and a dice cup. They had to race to complete tasks, such as roll five odd numbers. They seemed to enjoy it, although there was not enough time to get detailed feedback.

At the end of the session, because it was the last week of this half-term, I gave each child a gift to take home. I made these 2020 Rhombohedron calendars at home. I was testing different methods of attaching the parts of the net: PVA glue, glue dots, magnets. The winner was …. glue dots! The pdf is here.

 

I took all of the Sierpinski tetrahedrons the children had made home with me. I wanted to see if I could make one with three layers. I rearranged the parts, added two of my own, and came up with this, photographed from different angles:

 

 

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:

20200213_111535

Here is each one by itself:

20200213_11180120200213_11181820200213_11175120200213_11195120200213_111844

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.

20200213_112133

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.

20200213_111844

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.

20200213_112115