Video: The Platonic Solids and Assembling the NOAA Icosahedral Map of the Earth

the Platonic Solids (http://en.wikipedia.org/wiki/Platonic_solid).

viruses (since some have icosahedral capsids)

trusses (since the icosahedron is made of triangles). (Trusses were first mathematically studied by James Clarke Maxwell. Trusses are a good place to start when studying mechanics.)

The model platonic solids are made of drinking straw sides and (deformable) silicon rubber vertices. Despite the deformable vertics, the tetrahedron, octahedron and icosahedron (with triangular faces) are rigid. On the other hand, both the cube (hexahedron, with square faces) and the dodecahedron (pentagonal faces) are floppy. Early in the class I ask the kids if they can figure out why some of the Platonic solids are rigid and some floppy. For the first 10 years, I encouraged them try out the models themselves, during their spare time in the class and, if they have an answer, to let me know quietly (so not to let the cat out of the bag to the rest of the class). About half the time, some student figures it out (or already knows, I can't tell which). I had expected that most students would figure it out. As I discovered accidentally in 2011 (see below), the reason the kids weren't figuring out the answer, was that they had no spare time and I wasn't giving the kids enough time to play with the models.

The trusses and the earlier versions of the Platonic solids were made from toothpicks and hotglue. Making these models took several sunday afternoons. (Buy your toothpicks all at once; toothpicks bought a year later, at the same store, in the same type of box, were a different length.)

With about 30 models arrayed on various tables, one student asked in amazement if I'd made all of them. I said "yes, and it was great fun".

When I asked the kids to figure out why some of the toothpick and hotglue models were floppy and some were rigid, I first had to convince the students that some of the solids were intrinsically rigid and some were instrinsically floppy. With the glue providing some rigidity at the vertices, even for the floppy models, the usual answer was that the rigid solids had more glue. While the kids saw the glue as providing rigidity, they wouldn't look further to structural elements as the answer. As well the kids often broke the relatively fragile toothpick and hotglue models while testing their rigidity.

My first approach was to tell the kids that the rigidity wasn't coming from the glue. Quite reasonably kids don't trust adults, who are in charge, make arbitary rules and can make a kid's answer wrong any time they want. As all the kids could plainly see, the glue was providing (some) rigidity. It took several years before I saw the futility of expecting them to believe that the glue wasn't providing rigidity. I needed models with demonstrably floppy vertices. This led to the models with rubber tubing vertices in the video. Since I've changed over to these models, students have stopped proposing glue as the agent of rigidity.

In 2015, after displaying the relatively fragile toothpick and glue models in the front row of the table, I moved them behind the more resilent rubber tubing and drinking straw models, and let the kids play with the more resilient models.

Ask Lyn to get parent help. I didn't have this in 2018 and it slowed the class down, particularly at the beginning, when checking that the tab for the stand is right. So I need the assistant and a parent, as well as Lyn.

The class needs adult help. Most kids can't handle the manipulations by themselves. In the beginning of the class, someone needs to check that the kids have the stands done correctly before taping them.

Most of the kids don't have the tab pushed in right; it's too far in, not far enough in, skewed, or put in from the inside. Some fold the tab back on itself.

If there's only one person available (me), like happened in the 4th class in 2018, the whole class has to wait till I check each kid. This stage absolutely needs all hands on deck.

v1 (no longer relevant). At the suggestion of the teacher's assistant, I precut the cardboard sheets (for the v1 maps) (paper cutter/guillotine; a sharp one helps) removing extraneous cardboard and separating the legend and base from the map. This eliminated the first cutting step for the kids.

v2 Initially I pre-popped out the maps and handed the kids the whole piece of carboard, with the popped out pieces resting in the original locations.

From 2018: For the day with a late (10am) start, there is no lunch time, just the standard 25 mins between classes. Even with the partially popped out maps, it took me most of that 25 mins to completely pop out the maps and put them out and for Lori to put out the tape.

In 2017, I handed the kids only the popped out pieces and threw away the outer cardboard. Not having to collect the trash in class time saved a couple of minutes. It's too bad that education now is paced too fast for the kids to explore what they're doing, and be able to pop out their own maps (the class was originally 50min, with 16 students; now it's 40mins with 19 students. The 10 mins was taken from a couple of classes to allow the students to take an extra class in being well rounded. I'm sure we all agree that being well rounded is much better for the kids than understanding trusses.)

In the early years, I had held off putting out the maps until the kids were ready to start building the globes. I had expected the kids would be distracted by the map and not pay attention to my explanation of the platonic solids. However stopping the class to hand out the maps adds time to the class.

In 2015, following a suggestion by the teacher, I put out the maps before the class started. To head off the kids being distracted by the maps in front of them, in the introductory phase of the class, I first acquainted the kids with the maps by having them put their name on some blue spot (ocean) and on the stand, with marker pen. This seemed to give them time to satisfy their curiosity about the maps and they were happy to pay attention to my discussion about the platonic solids.

The first thing the kids need to understand is that the tabs are pushed in from the outside and that the tab, which now points inside, is taped over on the inside, where it can't be seen (from the outside). This is obvious to an adult, but not to the kids. If you start by having the kids taping the globe (with multiple tabs), an adult will have to cut the tape on the outward facing tabs to allow the tabs to be reinserted from the outside.

In 2015, in the first class, despite holding up a sample and showing them how to put the tab in from the outside, half of them got it wrong (==random), which means that none of them were listening (or my explanation was unintelligible).

Now, I first have the kids make the simpler stand. The stand has only one tab. A mistake here can be fixed relatively easily. Closing the loop that is the stand, requires the kid to put the tab in from the outside, and align the colours, so that the white is only just showing. I tell them to show me their stand before putting on the tape. By the last class of the day, I'd emphasised it enough that they'd all showed showed me the tab with the correct orientation for insertion before taping.

For the first 15yrs or so, I've been letting the kids pick up the tape dispenser and tear off the tape each time they needed tape. This requires them to put the globe down, pick up the dispenser and then when they have the tape, pick up the globe again.

I found that none of the kids knew how to tear off a piece of tape. This class must have been their introduction to the tape dispenser. They pulled the tape down straight, rather than tearing from one corner. This required enormous force and sometimes resulted in the tape dispenser flying out of their hands. I wasn't prepared for this and didn't know how to handle it.

The next year, in the preparation part, I showed them how to tear off tape. I told the kids to only tear off a piece of tape long enough to just cover the tab (1cm). Instead they tore off a piece about 4cm long. I expect they don't have the dexterity to pull off a short piece of tape. Initially I let this go.

In 2016, one of the assistants (Miss Connie), suggested that 15 short pieces of tape be pre-dispensed and attached at the edge of the table, with enough tape hanging horizontally over the edge for the kids to pick up the tape. What goes wrong now is that the kids, in their idle time, push the freehanging end of the tape down onto the vertical edge of the table, or else brush up against the tape, pushing it onto the table. We evetually put the tape on a side of the table away from the kids, where the kids would not brush up against it. At the beginning of the class, I asked the kids not to push the tape down, telling them that the ends are there so they can lift the tape off easily. When the time comes to assemble the globe, the table is too wide for the kids to reach across the table to the tape on the other side. Instead I have the kids walk around the table to use the predispensed pieces of tape.

In 2018 for the first class, we found that most of the tape got folded over the desk and the kids could no longer pick it up. Kids pushed against the tape while leaning on the table, or brushed up against it walking past. If they didn't quite pick it up right, it wound up stuck against the table. Clearly the idea was no longer working. Lori thought of some wooden boxes in storage, which she put the tape on. This worked quite well. I noticed that some kids could tear off tape, but they always pulled off a very long piece.

In 2019, I had forgotten about Lori's wooden boxes. For the first class I had put out tape on the setup day, on the outer edge of the table, away from the kids. This had lots of problems.

Lori brought out

Figure 2. tape boards

In the v2 map, the slots for the tabs are 1-D cuts rather than a real slot. Even an adult has difficulty on inserting the tabs, unless you expand/open the slot a little bit with scissors or a screwdriver. One of the problems was aligning and joining the edges. The kids should push the tab in till the colours match. If you push the tab all the way in, rather than stopping just a bit short, i.e. when the colours match up at the edges, then at the end, you can't close the icosahedron withough cutting of bits off the icosahedron. The resulting icosahedron is no longer symmetrical. With all the instructions being foisted on them, the kids had a hard time adding colour matching to their tasks.

In 2014 I found that telling the kids to leave the thinnest white line between the adjoining colours worked. Introduce this idea when the kids are making the stand. Make sure the tab is inserted from the correct direction (pointing inside the stand/globe) and there is a thin white line at the join of the two pieces before taping the stand.

In 2017 we no longer folded the maps along the creases, over the edge of the desk any more. The maps assembled, without the folding, just as easily as when the maps were pre-folded along the creases. Not doing the folding saved time. As well, we no longer had to deal with maps that had been folded 180° along the folds.

Several stages of checking are required (cut out, fold along all the black lines) so that the final map folds to a globe.

At the time I did the video, as soon as the first student was ready for the next stage, I stopped the whole class and demonstrated the next stage to everyone. This didn't work; the kids are busy with their efforts and quite reasonably don't have attention for much else. They certainly can't listen to instructions about a stage they haven't yet reached yet, whose problems they haven't seen. This is particularly so when the first student reaches the last stage of closing the globe. At this time some students are still back two stages - cutting out (for v1). I would have to repeat the taping instructions only a few minutes later, individually to confused students, as they reached the taping stage.

Instead, in 2011, as student(s) were ready for the next taping instructions, I walked over to the students and showed them individually how to apply the tape. The tape and the to-be-taped globe were in my hands, right infront of the students, who could see exactly how I did it. Initially only the first student was ready, then a few minutes later, a group of four more students were ready... Although this method required me to be in a constant frenzy, repeatedly explaining the next step to whichever student was in front of me, few students had to return for clarification, reducing the time on this step. (Your job is to make the class easy for them, not for you.)

Initial joins:

There are two rows of tabs to tape down; top and bottom. Pick one row and then start taping from one end to the other interlocking the pair of edges with the tab Do not start taping in the middle; it's hard to get your hand in to insert the tape.

Insert the tab (from the outside), carefully line up the colours on the maps, so the white cardboard underneath is only just showing. (The thinnest white line possible is needed.) Alignment of the edges (using the colours on the outside) is critical, or you can't close the globe. (You won't find this out till the end. If the globe doesn't close well, an adult has to cut pieces out of the globe.) Once the edges are aligned, put a piece of tape lightly on the tab (inside of the globe). Check that the map join is placed correctly. If you want to change it, an adult can lift the tape off the inside of the globe with a boxcutter, and the kid can do it again. If the alignement looks right, press the tape hard between your fingers.

As you work along the top/bottom, you'll find that accessing the inside of the globe needs longer fingers or more dexterity than the kids may have.

While the alignement of the colours at the edges of the join is critical, the placement of the tape in the inside is not; almost anything that holds the globe together will do. You can tape along or across the join of the edges.

Once you've done the top, invert the globe and start on the bottom, taping from the end.

Final joins

At the end you are left with 3 pairs of edges to join As well the three pairs of edges each have a tab in the middle. For almost everyone in the class, an adult will have to join these edges. We just used single sided tape on the outside of all 3 joins. It doesn't look great, but the kids get the class done in time.

If you want no tape showing, you need 6 pieces of double sided sticky tape. Each of these is inserted, after first slightly prying open each of the 6 gaps, to insert a piece of double sided sticky tape on the blade of a small screwdriver. This is OK for adults, but doesn't fly for kids in a time limited class.