How to make an icosahedron star

Icosahedron = 20 faced polyhedron. Star = pointy things! Materials: clear, straight drinking straws and curling ribbon. Prior skills needed: know how to tie a knot, know how to thread ribbon through straw.

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My colleague E showed me how to make these during the first year I taught 8th grade geometry. It was intended as a non-academic thing to do during class while state standardized testing went on. It still is, but I have brought it about to the regular 8th grade math classes. The accelerated 8th grade math classes sadly no longer has time for an activity like this.

We go to our local Smart & Final for the straws in the past. However, in recent years, they have either been out completely or don’t restock by the time we need them. Come on people, let’s not contribute to the Great Pacific Garbage Patch.

Not that my 8th graders use these straws terribly efficiently either. But that’s my own fault. I was pretty lax about it this year. Reasons for which I’ll go into another time.

Directions:

  1. Take 15 straws. Get an average estimate of how long one straw is by measuring a couple straws.
  2. Cut each straw in half. Trim straws that end up too long as needed. This step is the most important. It is more important to get the straws to be the same length than to find the midpoint of each one. If your straws end up slightly longer or shorter than half of the original length, it’s OK as long as you have 30 straws of the same length in the end. The half-way point is a guide to know approximately where to cut.
  3. Bundle the 30 straws with a rubber band, and mark your name on them. [This is a good place to stop for the day. Most students take 20-40 minutes on steps #1-3. Have a homework assignment ready for early finishers. If you have more time to continue, then by all means do so.] 
  4. Take a length of curling ribbon. [I limit my students to a wingspan’s worth of ribbon at a time.] Thread 3 of your cut-and-trimmed straws through the ribbon and tie it so that it forms a triangle. I personally like to form the triangle so that one end of the ribbon is much longer than the other. I’ll take the longer end and work on the next step without cutting the ribbon.

  5. Take 2 more straws and thread through the ribbon. Attach to your original triangle so that there are 2 adjacent triangles. NO TWO STRAWS should be parallel to each other – the shared side of the two triangles should also have a shared straw.
  6. Continue attaching 2 more straws to form an additional triangle until you have 4 triangles in a pac-man shape. [A lot of students get on a roll and continue until they form a hexagon. These students have gone too far and will need to undo some straws.]

  7. Attach one more straw to ‘close’ the pac-man’s mouth. Once you do this, the center of the shape will pop up to become the vertex of a pentagonal pyramid.

  8. Repeat steps 1-7 so that you have a total of 2 pentagonal pyramids. [This is another good place to stop for the day. I like to take a permanent marker and have all students mark their names on each of their pyramids PLUS the remaining bundle of straws.]

  9. Take one of the pyramids and attach triangular ‘legs’ on each side of the base. Leave the other one alone.

    IMG_0130

  10. Tie the ‘feet’ of each leg to each of the base vertices of the other pentagonal pyramid. Once all vertices are tied, you will have an icosahedron and ALL of your 30 straws should be used up.
  11. Next, decide if you what whole straws or half straws for the points of the star. You may use a mixture of whole and halves as well. If halves, take 30 straws and cut them in half again. If whole, take 60 straws. Bundle with a rubber band and mark with your name.
  12. Identify a triangular face on the icosahedron on which to attach a point for the star.
  13. Tie one end of a ribbon to one vertex of the triangular face.
  14. Thread 2 straws through it and tie the loose end to another vertex of the triangular face.
  15. Attach ONE straw to the remaining vertex of the triangular face, then tie to the other two straws.
  16. Repeat steps 12-15 for each of the triangular faces on the icosahedron.

    IMG_0133

  17. OPTIONAL: Leave a little bit of the ends at each point for curling.
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