## Hila Science Camp

## Dome Math

Geodesic Domes

Dome builders call this type of dome a **2V Icosa Alternate. **It is
created by fitting 4 triangles inside each triangular surface of an **icosahedron**.
What is an icosahedron? An icosahedron is one of the 5 solids created
by the ancient Greeks. Here are all five of them:

Can you name them? The last one on the right is an icosahedron, it has
20 triangular sides.

If you are really, really curious, follow this link to find out how
the triangles are fitted inside each triangle of an icosahedron - **Icosahedron Domes Explained!**

To create a dome similar to the one shown at top, you must create 40 triangles,
30 isosceles triangles and 10 equilateral triangles.

## Let's design a dome!

### Step 1:

Decide on the diameter of the dome you would like to create. Let's build
a small model, 30 cm in diameter.

### Step 2:

Determine the size of the triangles needed. The triangles we are going
to create, require glue tabs on their edges, they will look like this:

The 10 equilateral triangles have each side equal to a length "A". To determine
"A" we use a number called a "**Chord Factor**".

The chord factor for "**A**" is **0.61803**. To determine the length
of "A" multiply the chord factor times the radius of the dome you are designing.
Remember that radius = 1/2 of diameter. Our dome has a diameter of 30 cm
and a radius of 15 cm.
A = radius of dome x 0.61803

A = 15 cm x 0.61803

A = 9.27045 cm

A=9.27 cm

The 30 isosceles triangles have one side "A" and two sides "B". We know
"A" is 9.27 cm, to calculate "B" we use a different chord factor, the cord
factor for "**B**" is **0.54653**

B = radius of dome x 0.54653

B = 15 cm x 0.54653

B = 8.19795 cm

B = 8.20 cm

### Step 3:

To construct this dome you must create triangular elements using the dimensions
"A" and "B". Draw a 30 cm diameter circle on a solid cardboard base then follow
the** instructions for constructing the 50 cm
dome.**
**You can create a dome of any size, just multiply radius times the chord
factor. Then follow the assembly sequence for the 50 cm dome.**

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Science Camp: http://hilaroad.com**