To make an equilateral triangle from flexible straws, join them together short end to long end, using the flexible parts as the corners. The corner of a triangle is called a vertex.
The best way we could find for joining the straws together was to squish one end flat against a hard surface using our thumbs. Then put a crease down the center of the flat end using a butter knife. Pinching the crease together, slide the small end into the long end of another straw, like an arm going into a sleeve.
Step 1: Start Joining Together Triangles to See What Happens
We discovered that the straws stayed together if you put the hot glue blobs on the joints, where the straws come together. The hot glue slightly melted through the outside of the place where the straws came together, making them hold.
At this stage, we had to blow on the glue to get it to set while holding the straws together firmly. Later on, we discovered a better way.
Step 2: Start Joining Together the Faces, Run Out of Straws
This made us realize we might be able to built a complete geometric solid! Then we looked down at our pack of straws and noticed that we were already running out.
Step 3: Figure Out How Many More Straws to Buy
Each triangle had three straws, and each face had five triangles, so we counted in groups to find that each face contained 15 straws. We had built 4 faces, so that was 4 groups of 15, or 60 straws.
It looked like it was going to take another 2 faces, or a total of 6 faces to make a half of the solid. That meant it was going to take 12 faces to make the complete solid.
We decided to count in groups of fifteen using tally marks on paper and found that 12 groups of 15 was the same as 180.
We had already used 60 straws and we needed to make sure to buy enough to finish the solid, so owe had to find out how many more to buy. This led to finding the difference between 180 and 60, which was tricky because our mathematician was only 6 years old. We eventually found that we were going to need 120 more straws.
Step 4: Get Burned by Hot Glue and Discover a Better Way
Step 5: Get the Whole Family Making Triangles
Step 6: Adjust Sides As You Close It Up...
Step 7: Review the Math, Look It Up, and Take It to School
5 groups of 3
6 groups of 15
12 groups of 15
60 groups of 3
3 groups of 60
Once we realized it had 60 triangular sides, we did some internet searching and discovered we had built a pentakis dodecahedron.