### An **icosahedron** is a **polyhedron** that has twenty triangular **faces**. A **stellated icosahedron** has each of those faces raised to a** triangular pyramid**. Wow! There’s a lot of big words in that sentence!

### Spark your math thinking!

- Set up your math mini spark recording page: #57: Polyhedron
- Find out more about polyhedrons. Take notes on your recording page.
- Make a Modular Origami Stellated Icosahedron. You will need 30-35 pieces of 3 X 3 paper or origami paper.
- Watch this video to help you get started.

5. Work on your Modular Origami Stellated Icosahedron. Be patient. It takes practice to make a shape this complex. Take a picture of your project and add it to your recording page.

6. Respond to this prompt: How is origami related to math?

7. OPTIONAL: Find instructions for math other polyhedron. Here is a site to try. Take a picture of your project and add it to your recording page.

8. OPTIONAL: Find instructions to make an origami animal using the WWF Together app on your iPad.

9. Share your math mini spark recording page and your with your teacher/EY coordinator.

There are 5 regular polyhedron which are also called Platonic Solids. I watched a BrainPop video and they called them “Dice of the Gods” in the video. I explored some other polyhedron and thought the names were weird like Trapezoidal Icositetrahedron and Rhombic Triacontahedron. You can find animated models by going here: Math is Fun

It surprised me that not all polyhedrons follow the basic formula, like I was taught in Pre-algebra. Also, the torus is sort of like a ring without edges at all. How could someone discover the Mobius strip? Probably someone named Mobius. The Cubohemioctahedron is quite confusing. Tongue twister, huh? Technically, it is a polyhedron because the definition says “…that is usually joined at the edges.” I may look into that later.

Thanks for the hard work you do! My class will start doing these math minutes next week. These shapes are great ways to combine math and art.

This is a great website to learn on. Thanks for your help.

A polyhedron is a solid with flat faces

I learned how to make an Icosahedron!!!!!

A polyhedron is a shape with flat surfaces. Polyhedron is from Greek roots with a very straight forward name. It could be anything from a cube to dodecahedron. A dodecahedron has many sides. Others may be more exotic with how many faces it has.

I learned that 3D shapes are also known as polyhedra.

I learned that in Polyhedrons, there are no curved faces. There are points only, no curves what-so-ever.

Is it really true that all solid figures follows the simple equation: Faces + Vertices – Edges= 2? I’ve heard of non-Euclidean geometry, do those rules still hold up then‽

That’s a good question Matthew! I bet if you do a little research, you’ll find the answer to your question. Can you provide an example of that equation?

I am guessing that a polygon is the same thing as a polyhedron. I had no idea that there were two names for that. I was wondering if anyone had tried to make a Snub Dodecahedron, because I tried to make a plain Dodecahedron and that was hard enough. You can try to make your own polyhedron at http://www.mathsisfun.com/geometry/model-construction-tips.html

Hi Caleb-There is a difference between polygons and polyhedron…polygons are 2-Dimensional and polyhedron are 3-Dimensional.

It is interesting that the number of faces + the number of vertices – the number of edges = 2, but some shapes like the icosahedron only = 1.

I never knew that cubes were polyhedra! It’s very cool to know that polyhedrons make up so many objects in our everyday geometric society. Just think that 100s of years ago, mathematicians developed polyhedra! Who even thought of such a word? I really wish to know more about these great geometric shapes.

Polyhedron do NOT have any curved parts in any way.

And faces plus vertices minus edges equals two, but in some cases they only equal one.

And there are hundreds of polyhedrons in many ways like pyramids and more.

I learned that a stellated icosahedron has each of those faces raised to a triangular prism.

The faces, vertices, and edges are needed to make polyhedron. The vertices are corners, the edges are all the lines used, and the faces are the flat surfaces. That’s how it’s related to math.

I learned that a polyhedron is Greek for many faces and the formula: The number of faces plus the number of vertices

minus the number of edges equals 2.

I learned that polyhedron is Greek for many faces and the formula: The number of faces plus the number of vertices

minus the number of edges equals 2.

I didn’t know that a duodecahedron had 12 faces.

I learned so much about all the polyhedron and now know there are so many different polyhedrons, like the dodecahedron has twelve faces.

What is the most sided polyhedron?

I learned that a polyhedron consists of three dimensional solids connected at the edges and that it is from the greek works poly many and the European hedron or seat

I learned that polyhedrons are 3-D shapes with flat sides. There are 5 normal, or basic polyhedrons which are called Platonic Solids. Polyhedrons are difficult and are not easy to understand considering I’m only 10, but I managed to follow along and learned a few new things.

I didn’t know there was such a confusing shape that existed, and if I did I would’ve never thought it could be made with paper!