Math = Love: Icosahedron Ornament Balls Tutorial

Saturday, May 31, 2014

Icosahedron Ornament Balls Tutorial

To help celebrate the end of school, I declared the day before the last day to be "Bring Your Sister To Work With You Day."  I cleared it with my principal beforehand.  My sister is my best friend, and I've told my students lots of stories about her over the course of the school year.  So, they've been begging to meet her for months.  Since she is in college, her semester ends a week or two before ours.  This allowed her the opportunity to come and visit.

My Sister and Me

My kids were amazed by my sister.  The look on students' faces as they walked in the room and saw my sister and me was priceless!  Some even mistook her for me.  Are you guys twins?  Nope, we're three years apart. This is so weird!  You guys even sound the same!  Though, one student said that my voice was a little higher than my sister's.  And, another student in a different hour claimed that our voices were almost the same, but my sister's voice is a bit higher than mine.  I'm not sure who to believe.  We also heard from multiple students that we have the exact same laugh.  That's good to know.  Another student claimed, in amazement, that we also dress alike.

The fact that they had to call us Ms. Hagan was almost too much to handle.  One class decided to differentiate between us by calling me Ms. Hagan 1 and my sister Ms. Hagan 2.  My sixth hour referred to my sister as Ms. Hagan and myself as Ms. Nagah (which is Hagan backwards, by the way!)  My fifth hour wanted to refer to me as the original Ms. Hagan, but that implied that my sister was the imposter Ms. Hagan which did not go well.  :)  Then, there was the student who decided they should just rename us Tweedledee and Tweedledum.  When she suggested that I could be Tweedledum, I asked her what she was implying.  Overall, it was fun to introduce them to my sister.  Though, I'm pretty sure that they like her way better than they like me.  

She didn't just come and visit.  She also brought a project to do with my kiddos.  Lots and lots of circles.  Hundreds of them!  

Scrapbook Paper Circles

She also brought curling ribbon and equilateral triangles cut out of white card stock.  She brought some glue sticks, and I also retrieved some from my cabinet.


While waiting for school to start, she made me several tiny origami flappy birds.  Sadly, the wings of the tiny flappy birds barely flap.   But, they were still cute!

Miniature Origami

Our project for the day was to make an icosahedron ornament ball.  My sister and I both made these for the first time as 7th graders in Mrs. Seller's Pre-Algebra class.  We made ours out of recycled Christmas cards.

Here, some students proudly display their finished products.

The Finished Products

After folding lots of circles/triangles, the students glue them together to form an ornament ball.

Folded Triangles/Circles

Here are the icosahedron ornament balls in the process of being assembled.

The Assembly Process

Here are some ornament balls that my students completed.

Finished Products

So, how do you make your own?  

If you're only making one, you could probably get by with cutting out your circles by hand.  Each icosahedron ornament ball takes 20 circles.  My sister used a circle punch to punch out her circles and save her sanity.  She used a 2 1/4" circle punch, but any size circle will work.  Larger circles will produce a larger ornament ball.  

Circle Punch - An Amazing Tool!

She punched the circles out of random leftover scrapbook paper and these booklets of photo mats that she picked up at Wal-Mart for around three dollars.  The small size made manipulating the punch much easier.

Photo Mats

You're going to need to cut an equilateral triangle template whose points rest on the edge of your circle.
Equilateral Triangle Pattern

Lay the template on top of each circle and begin folding over the edges.  
Folding Over the Edges

After folding over two of the edges, it is usually easiest to remove the template before folding over the final edge.  This reduces the chance that your triangles will not match up when gluing.

Two Down - One to Go! 

Folds Completed

A small gap in the center of triangle is fine.  Gaps on the vertices of the triangles are bad.  Pretty soon, you'll have a pile of triangles.  Remember, you need 20 of them!

Waiting to Assemble

My sister made two partial pieces to demonstrate the construction process to my students.  I thought this was a brilliant idea.  She's going to definitely make a great art teacher!

First, students need to take five of their triangles and glue them together to form a dome.

Completed Top Dome

You are actually going to need to make a dome for the top of the ball and a dome for the bottom of the ball.  The top dome needs a curling ribbon hanger.  Take a piece of curling ribbon, knot it, and place it in the center of the dome before gluing the last two triangles together.

We had lots of different colors of curling ribbon to choose from.

Curling Ribbon

The bottom dome is created in the same way, just without the ribbon.

After using five pieces to make the top dome and five pieces to make the bottom dome, you should have ten pieces left.

Glue these ten pieces together, inverting every other triangle, so that the pieces form a line with a flat top and flat bottom.

Here, my sister glued five pieces together to demonstrate the process to the class.

Sample of How to Construct Sides of Icosahedron Ball

At the end of the day, we took my sister's sample pieces and added more pieces to form a complete ball.  Here's the top and bottom domes.

Top and Bottom Domes

And, here are the ten pieces that will make up the middle of the ornament.

Middle of Ornament

The best way to go about this next step is to turn over your long strip of triangles and apply glue to the top or bottom of the strip.  Then, begin attaching each piece with glue on it to a section of one of your domes.  Then, add glue to the remaining pieces and attach the other dome.  
Applying Glue to One Side of Strip

Here's a picture my sister snapped of me in the process of gluing my icosahedron ornament ball together.

Moi :) 

Here are pictures of my finished ornament!  So pretty!

The Finished Product

Showing Off My Creation

By the end of the day, I had gained a collection of left behind ornament balls in the back of my classroom.  Well, I guess one of these was mine and one was my sister's, but the rest of them were student creations that didn't make it home.


If you wanted to make this more math-related, you could have students cut their circles out of colored cardstock and decorate each circle to reflect something that they learned this year.  I'm pretty sure that's not an original idea.  I thought I saw it on Pinterest once, but I can't find it.

You could take Tina Cardone's Fan Posters Project and turn it into Fan Icosahedron Ornament Balls.  Pass out circle templates and have each student write affirming statements about their classmates on a circle.  Sort the circles by student.  Then, have the students assemble their own ornament ball that is covered with words about them.  Maybe students would be more likely to keep them if they were customized?

I ended up giving all the leftover ornaments to one of my students who is going to use them to decorate her bedroom.

I could also see this as a culminating geometry project.  Each triangle could be decorated with a different theorem?  Or geometric vocabulary word and illustration?  Perhaps this could be turned into an activity of geometric construction?  Use a ruler and compass to construct the necessary pieces without a template?    


  1. I have done these with 8 circles in the past and used it as an intro activity at the beginning of the year where the students answer 8 get to know you questions in the center triangle area. Great project!

    1. I like this idea! And, only having 8 circles would make this a much less time consuming task! With 20 circles, I had students struggling to finish in our 50-minute class periods. Thanks for sharing!

  2. This seems like a great way to introduce Euler's formula for 3D shapes: the number of faces and edges become obvious when they're the number of circles and the number of 'glued together curvey bits'. I've had students make Icosahedra (is that right?) out of nets before, but they're always a bit too fiddly and definitely don't look as good as yours!

    1. Ooooh! I never thought of introducing Euler's formula this way. What a great idea!