Creating a Geodesic Dome

1. Geodesic Domes

Ever see a geodesic dome or sphere and wonder how they are made, or if there's something more behind the mathematical beauty of these shapes?

Let's learn a bit about geodesic domes, and then make one ourselves!

2. Geodesic Dome basics

Most geodesic domes start with the icosahedron, which has 20 sides, each made up of a equilateral triangle (a triangle that has 3 equal sides).

Icosahedrons are also known as d20's by gamers before video games, but that's for another tutorial.

2.1. Turning a icosahedron into a dome

To turn a icosahedron into a dome, we'd want to "pull out" each of the triangle sides of the icosahedron to become more spherical.

Here you can see by adding a smaller triangle, and pulling that triangle out, we can get closer to a sphere! If we were to add a smaller triangle inside of each side of our friendly icosahedron, we'd end up much closer to a sphere.

2.2. Geodesic Frequency

Geodesic domes are named by their frequency. What does frequency mean? Let's start with our favorite icosahedron.

On the left, the icosahedron is made up of 20 triangle sides,.

The next shape has each triangle face of the icosahedron divided into a smaller triangle. Since the triangle is divided, it's known as a 2 frequency dome.

Similarly, the next sphere is has 3 subdivisions, resulting in a 3 frequency sphere.

Finally, we see a 4 frequency geodesic sphere - the basic triangle has four subdivisions.

2.3. The basics of a 2 frequency geodesic dome

The dome we'll be creating is called a 2 frequency geodesic dome.

There are 2 different lengths of posts in a 2 frequency dome. In this diagram we've labeled the lengths A and B.

Can you still see the icosahedron in the dome? (hint: look at the red "B" posts!)

3. Supplies

Let's check that we have everything we need.

You will need:

Straws (65)
Pipe cleaners in 2 colors, approximately 10 of each color.
Scissors
3 plastic cups
2 sharpies of 2 different colors.
1 ruler

4. Cutting our straw posts

You will need 35 straws that are 12cm long (we'll call those "A" straws).

And you'll need 30 straws that are 11cm long (let's call them "B" straws).

5. Label two plastic cups

Label a cup A and another B. It's important to keep your A straws and B straws separate, so be careful not to mix them. Using these cups should help!

6. Cut your A straws

Using the ruler, measure 12 centimeters (120 millimeters) and mark it with a marker.

6.1. Make your cut

Using the scissors, cut on the mark you just made.

6.2. Mark the A straw

Remember, we need to keep our A straws separate from our B straws. Choose one color marker to use for marking all the A straws, and draw a dot on the straw.

6.3. Mark your A cup with the same color

Mark your A cup with the same color. Now place your A straws in the cup as you cut them.

6.4. Left over cup

Place the extra straw cut off in another cup. We won't need these, but they can be reused.

6.5. Measure, cut and mark the rest of the A straws.

Remember, we need 35 A straws, each 12 cm long and marked.

7. Cut your B straws

Measure your B straw (11 centimenters or 110 millimeters) and mark, just like you did for the A straws except the B straw is 1cm shorter.

7.1. Cut on the mark

Using scissors, cut on the mark.

7.2. Mark the B straw

Using a different color marker than the A straws, put a mark on the straw.

7.3. Place the finished B straw in your B cup

7.4. Measure, cut and mark the rest of the B straws.

Remember, we need 30 B straws, each 11 cm long and marked.

8. Creating the base

Let's refer back to our 2 frequency dome diagram.

The bottom base is made of 10 "A" straws.

8.1. Using pipe cleaner, create a loop of 10 A straws

Thread the A straws through pipe cleaners to make a 10 long loop.

You can splice, or lengthen pipe cleaners by twisting the ends together.

9. Creating the first ring of triangles

Now that we have the base, we'll create the first set of "B" triangles on our dome.

9.1. Thread two B straws

Thread two B straws in a pipecleaner.

9.2. Add the triangles to the base

Skip over every other section, so you've added 5 B triangles with a space between them.

10. Adding A triangles

Let's fill in those gaps by adding the A triangles

10.1. The base after adding the A and B triangles.

You should now have a very large and floppy crown.

11. The first parallel ring

Now we add a ring of B straws.

11.1. After adding the B straws

12. The next layer

Now we add a ring of B straws.

12.1. Adding the next layer

Find where 4 B straws connect, and add another B straw pointing upwards.

12.2. A close up

Notice you now have a 5 pointed star shape of B straws?

13. Adding A triangles

Now we connect the B straws with A triangles

13.1. After adding the A triangles

13.2. A close up

You should notice it's starting to feel mor like a dome!

14. Adding the A top ring.

Now we add a top ring of A straws.

14.1. After adding the top ring

14.2. A close up

15. Adding the top

Now we'll add 5 B straws to form the top!

15.1. After adding the top

16. Finished Dome

Congrats! You created the dome.

To finish the dome, you can wrap the extra pipe cleaner that's sticking out around the intersections.

17. Taking it to the next level

If you have time, try the following:

Can you:
Complete the other side of your dome to make a full geodesic sphere?
Connect two domes together with a geodesic tunnel?
Create a 3 frequency or 4 frequency dome?
Scale our dome up and make one 2 or 3 times as large?
Make a dome out of other materials - maybe toothpicks, rolled newspaper, sticks, or something else?

18. References

http://geo-dome.co.uk/article.asp?uname=domefreq

http://nrich.maths.org/content/id/8266/geodesic_dome_worksheet.pdf