We had no idea what we were making at first.  We were noodling around with a pack of straws, and we discovered that it was that it was possible to make colorful triangles.  The sides of these triangles were all the same length.  We learned that triangles whose sides are all the same length are called equilateral triangles.

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 decided to try using our hot glue gun to stick triangles together with their vertices all sharing a single point.   As we added triangles, eventually we were able to make a kind of 5-faced squat pyramid shape.   We thought it was pretty.

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

Once we had made two squat five-sided pyramids, we joined them together along a shared side.  When we had made a third, we realized that it would fit into the space where two others came together.   We noticed that the three faces had started to make what looked like a part of a sphere...kind of like a giant piece of orange peel.

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

We looked at what we had built already, and found a handy way to count up the straws we had used.

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

Our six year old apprentice eventually got burned (not badly) by hot glue, which led to a discussion of why water is so good at absorbing heat.  She then suggested that we put a bowl of water on the table and dip our fingers in it to help cool down the glue.   The method worked brilliantly.  The glue sets right between your fingers.  Whenever you get uncomfortable, just dip them back in the cool water.  Amazing suggestion from a child.

## Step 5: Get the Whole Family Making Triangles

Making 60 triangles from straws is a great job for a group of kids of different ages.

## Step 6: Adjust Sides As You Close It Up...

The shape should close itself as you work.  Getting all the corners to match up can get a little wonky because of inconsistencies in the lengths of the sides.  Fortunately, you can adjust the lengths of the sides that haven't been glued yet, which makes it super easy to compensate for any weirdness.

## Step 7: Review the Math, Look It Up, and Take It to School

We had a lot of fun going through the math for counting the straws in lots of different ways, all of which led us to count number of groups of different numbers.

5 groups of 3
6 groups of 15
12 groups of 15
60 groups of 3
3 groups of 60
etc.

Once we realized it had 60 triangular sides, we did some internet searching and discovered we had built a pentakis dodecahedron.