# 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.

Year 1 boy. Truncated Tetrahedron; Cube; Octahedron.

Year 5 boy. Cube; Octahedron; Truncated Tetrahedron.

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

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

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

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

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