Search term: archimedean

Playing with some Archimedean solids

Today’s project was inspired by two books:

Test

and

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I leave for a week-long trip to Scotland tonight and was looking for a project that would be both fun and relatively easy to do. By luck I piced up Dave Richeson’s book and it fell open to a picture of some ARchimedean solids which gave me the idea for the Zome project.

We have done some projects on these shapes previously via Zome Geometry. Here’s the full collection:

Our projects mentioning Archimedean solids

This shape was particularly fun:

Snowman

Today we started the project by looking at the Wikipedia page for Archimedean solids:

Next we went to talk about the shapes we built – starting with the truncated dodecahedron. It was fun to talk about the symmetries and also count the number of faces, vertices and edges.

Sorry this (and the next) video is so out of focus – I chanced the focus to film the computer screen for the last video and forgot to change it back.

Now we moved on to the truncated icosahedron:

The last Archimedean solid we looked at was the Rhombicuboctahedron:

Finally we looked at an example from Richeson’s book of a solid that is not an Archimedean solid, but still has most of the properties -> called it a smushed icosahedron:

This project shows how a Zometool set can make some advanced ideas in math accessible to kids. If there was one

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Playing around with some Zometool Archimedean Solids

[fast write up this morning, sorry, had to get out the door about 30 min after we finished]

Last night I asked the kids what they’d like to do for our Family Math project today and the kids asked for a Zometool project. Flipping through Zome Geometry last night I found a neat section about Archimedean solids.

Despite one unfortunate goof up by me, playing around with these shapes made for a pretty fun project. I love that the Zometool set gives you a relatively easy way to hold shapes like these in your hand.

We started off talking about the definition of an Archimedean Solid and working through some of the question in the book:

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With that introduction, we took out the Zometool set and tried to build a few just from the description of the faces. The first solid that we tried was the icosidodecahedron and the kids seemed to have a fun time building it and talking about it:

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Next up was a rhombicoidodecahedron. Same thing here – fun to build and fun to talk about:

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The next shape I asked them to try to build was a snub cube. This was a challenge. One factor contributing to the challenge is that this shape can’t be built using the Zome pieces. Whoops – sorry boys!

After this goof up by me, we returned to the two previous shapes to count the faces, edges, and verticies. Tured out to be a nice counting exercise and hopefully brought the project back to being fun after 10 minutes of trying to do something that was impossible 🙂

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A fun coincidence with an Eduardo Viruena creation

I got some great feedback from Eduardo Viruena on the project we did with one of his math designs:

A short project inspired by a Holly Krieger tweet

One of his other designs he pointed me to was this one:

A small stellated dodecahedron approximated by dodecahedra

Here’s his picture:

Dodecahedra.jpg

I printed it over the course of the day (took about 6 hours) and showed it to my younger son when he got home from school. Here’s he described the shape, including noticing one very interesting pattern that he thought would form an Archimedean solid:

It turns out that the shape he saw would indeed be an Archimedean solid. In fact, it the exact solid we did a project on a few weeks ago!

Here’s that project:

Revisiting our Zometool Snowman

Which was inspired by this tweet from Eli Luberoff:

The Snowman is still up in our living room (which I’ll attribute half to coincidence and half to laziness . . . . ) so we looked carefully at the two shapes:

Amazing what kids notice when they look at mathematical objects!

Revisiting our Zometool Snowman

When we first moved into our house we did a couple of fun and large Zometool projects because we didn’t have any furniture 🙂

This week I saw a fun tweet from Eli Lubroff that reminded me of one of those projects:

Here’s a part of that old project 🙂

Snowman

Today we revisited that old snowman and had the boys talk about each of the Archimedean solids in the shape. This is a fun project – not just because the shapes themselves are cool – but you get a nice opportunity to talk about counting and symmetry. You’ll see in the videos that my older son is a bit more comfortable with the idea, but my younger son seems to catch on by the 3rd video.

Here’s a link to all of the Archimedean solids on Wikipedia:

The Archimedean Solid page on Wikipedia

And here’s our project:

First the bottom of the snowman – the Truncated Icosidodecahedron

Next was the Rhombicosidodecahedron

Next was the Icosidodecahedron

Finally the Archimedean Solid Snowman 🙂 Two years later and he still fits!

Definitely one of my all time favorites and a really fun way to discuss counting and symmetry!

Tiling 3 dimensional Space with our Zometool set

A while back we did a fun project from Zome Geometry about tiling the plane with different shapes you can make out of Zome struts – these pentagons, for example:

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Zome Tilings

 

Yesterday we did another project out of Zome Geometry looking at Archimedean Solids:

A Quick Zometool Project

Today we sort of combined the two projects and looked to see if the truncated octahedron (and our smushed truncated octahedron ) could tile 3 space. We have looked at 3d tilings previously, too, so the 3d tiling idea isn’t totally new to the boys:

Revisiting the Rhombic Dodecahedron

The main difference between today’s project and the one using the rhombic dodecahedron is that building the truncated octahedron is a tiny bit more difficult because of the connections with green struts are slightly more complicated.

After we finished the builds this morning we talked about the shapes. First up was the truncated octahedron:

Our incorrectly built truncated octahedron also could tile space – that was sort of a miracle! It turned out to have a second use, too, as it was easier to see some of the symmetry in the shape because it had struts with different colors:

After seeing some of the symmetry in the “smushed” truncated octahedron, we went back to the first collection of real ones to see those same symmetries:

Definitely a fun (and challenging) project today. I love how the Zometool set opens up the world of 3D geometry for kids.

A quick Zome project

The boys were running out the door early today to go skiing and we were looking for a short project this morning. I told them to go grab “Zome Geometry” and find something that they’d like to build.

 

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Turned out to be a nice little activity for them since they are getting to the point where they can complete most of the project on their own.

They ended up choosing the section on Archimedean Solids and built two – here are their thoughts:

(1) The Truncated Octahedron:

(2) The Icosidodecahedron

So, a fun project, and, as usual with Zome constructions, it is neat to hear kids talk about 3D geometry. It was also neat (though an accident) to see the kids build the truncated octahedron incorrectly the first time and then figure out the right way to build it.

I wish I could have seen more 3D geometry when I was a kid – it is so neat 🙂

A little Zome geometry in our new house

I was playing around in our Zome Geometry book looking for a project today. Stumbled on chapter 12 in the book about Archimedean solids. Unfortunately as we are currently transitioning between houses, I didn’t have any green zome struts. Luckily we found a few shapes that we could make using only blues.

The goals for today were:

(1) Construct some shapes from seeing their pictures on the computer, and
(2) Have them explain the things that they noticed about with these new shapes.

That noticing and wondering led to the creation of this awesome “snowman” at the end of the project:

We started with the Icosidodcahedron – seen here on Wikipedia:

The Icosidodecahedron on Wikipedia

First what they thought of the shape:

 

Here are their thoughts after building it:

 

Next up was the Truncated Icosidodecahedron seen here in Wikipedia:

The Truncated Icosidodecahedron on Wikipedia

Here is their initial reaction to the shape:

 

and their thoughts after building it – relating these first two shapes led to an interesting conversation.

 

 

The final shape we looked at was the Rhombicosidodecahedron, seen here on Wikipedia:

The Rhombicosidodecahedron on Wikipedia

Here’s their initial reaction to the shape:

 

and their thoughts after building it:

 

Finally – just for fun – here’s the snowman 🙂