# Geodesic Dome Frequency Examples

1v Dome
2v Dome
3v Dome

4v Dome
5v Dome

6v Dome

1 Frequency Dome

2 Frequency Dome

3 Frequency Dome

4 Frequency Dome

5 Frequency Dome

6 Frequency Dome

Dodecahedron
Octahedron
Tetrahedron

## A 1 Frequency, or "1v" Dome is an Icosahedron.

1v Icosahedron Dome

### A Good Way to Use a 1v Dome

A 1v Icosahedron Dome Shelter
by Geodesic Buildings, Malaga, Spain.

## But the problem with a 1v Dome is...

### "Tessalation" Increases Geodesic Dome Frequency.

"Tessalation" means that you are breaking up a flat surface into smaller "tiles" with no gaps or overlaps.

The tessalation of the triangular face of an Icosahedron into smaller triangles increases the Geodesic Dome Frequency.

1 Frequency
1 Edge, 1 Triangle
(No Tessalation)

2 Frequency
2 Edges Each Side,
4 Triangles

3 Frequency
3 Edges Each Side,
9 Triangles

4 Frequency
4 Edges Each Side,
16 Triangles

5 Frequency
5 Edges Each Side,
25 Triangles

6 Frequency
6 Edges Each Side,
36 Triangles

### Let's Tessalate a 1v Dome into a 2v Dome.

##### Each triangle of the 1v dome is "equilateral", which means all sides are the same length.

1v / 1 Frequency Dome

A 1v Dome Uses Equilateral Triangles.
All sides are the same length.

##### The Blue "A" and Red "B": struts (edges) of the 4 new triangles represent different lengths.

A 1v Triangle with no Tessalation.

All edges are the same length

A 1v triangle becomes a 2v triangle when tessalated into 4 triangles.

The red and blue edges (or struts) represent different lengths.

## 1 Frequency Geodesic Dome

The 1 Frequency Geodesic Dome Has 1 Edge for Each Edge of the Icosahedron.

The 1 Frequency Dome has 1 Edge and 1 Triangle for each Face of the Icosahedron.

The 1 Frequency Dome is an Icosahedron.

## 2 Frequency Geodesic Dome

The 2 Frequency Geodesic Dome Has 2 Edges for Each Edge of the Icosahedron.
1 Vertex On Each Edge is Pushed Outward.

The 2 Frequency Dome has 2 Edges on Each Side and 4 Triangles for each Face of the Icosahedron.

This is how the 2 Frequency Dome is derived from the Icosahedron.

## 3 Frequency Geodesic Dome

The 3 Frequency Geodesic Dome Has 3 Edges for Each Edge of the Icosahedron.
2 Vertices On Each Edge Are Pushed Outward.

The 3 Frequency Dome has 3 Edges on Each Side and 9 Triangles for each Face of the Icosahedron.

This is how the 3 Frequency Dome is derived from the Icosahedron.

## 4 Frequency Geodesic Dome

The 4 Frequency Geodesic Dome Has 4 Edges for Each Edge of the Icosahedron.
3 Vertices On Each Edge Are Pushed Outward.

The 4 Frequency Dome has 4 Edges on Each Side and 16 Triangles for each Face of the Icosahedron.

This is how the 4 Frequency Dome is derived from the Icosahedron.

## 5 Frequency Geodesic Dome

The 5 Frequency Geodesic Dome Has 5 Edges for Each Edge of the Icosahedron.
4 Vertices On Each Edge Are Pushed Outward.

The 5 Frequency Dome has 5 Edges on Each Side and 25 Triangles for each Face of the Icosahedron.

This is how the 5 Frequency Dome is derived from the Icosahedron.

## 6 Frequency Geodesic Dome

The 6 Frequency Geodesic Dome Has 6 Edges for Each Edge of the Icosahedron.
5 Vertices On Each Edge Are Pushed Outward.

The 6 Frequency Dome has 6 Edges on Each Side and 36 Triangles for each Face of the Icosahedron.

This is how the 6 Frequency Dome is derived from the Icosahedron.

### Here is the "Secret" of How the Lengths of the Tessalated Triangle Cause the Vertices to be "Pushed Outward" into a Sphere.

##### For a 16' Geodesic Dome, this means the Red Struts would be 4' 5" in length, and the Blue Struts would 5' in length. That is quite a difference!

2v Dome Panel

2v Dome Edge Lengths
for a 16' Geodesic Dome

### The Other "Secret" is...

##### So, it is a combination of these 5-way and 6-way connections and their 72 degree and 60+ degree angles, along with the shorter Red edges on the outside of the Icosahedron triangle, that will bend each Icosahedron face into a 3 dimensional curved surface to create a portion of the Geodesic Dome.

2v Dome Panel with Angles

2v Dome Panel applied to a Spherical Surface

### Here Are 6 Examples of the Curvature of Dome PanelsWhen the Length of the Struts are Changed.

(Notice the pattern that the shortest struts are always on the outside of the triangle, and the longest struts in the center of the triangle.)

### 2v Dome Example

##### For building a 16' Diameter Dome, the edge (strut) lengths will be:

Blue (A): 5'
Red (B): 4' 5"

Curved 2v Dome Panel on a spherical surface.

Flat 2v Dome Panel Diagram

### 3v Dome Example

##### For building a 24' Diameter Dome, the edge (strut) lengths will be:

Blue (A): 5'
Yellow (B): 4' 10-3/4"
Red (C): 4' 2-3/4"

Curved 3v Dome Panel on a spherical surface.

Flat 3v Dome Panel Diagram

### 4v Dome Example

##### For building a 30' dome, the edge (strut) lengths will be:

Red (A): 3' 10-3/4"
Yellow (B): 4' 6-1/2"
Brown (C): 4' 6-3/8"
Black (D): 4' 9-3/4"
Blue (E): 5'
Orange (F): 4' 7-1/2"

Curved 4v Dome Panel on a spherical surface.

Flat 4v Dome Panel Diagram

### 5v Dome Example

##### For building a 38 Diameter Dome, the edge (strut) lengths will be:

Red (A): 3' 9-1/2"
Yellow (B): 4' 5-1/2"
Brown (C): 4' 3-3/4"
Green (D): 4' 8-3/4"
Orange (E): 4' 10-1/2"
Black (F): 4' 8-1/4"
Blue (G): 5'
Purple (H): 4' 5-1/8"
Gray (I): 4' 8-1/4"

Curved 5v Dome Panel on a spherical surface.

Flat 5v Dome Panel Diagram

### 6v Dome Example

##### For building a 46' Diameter Dome, the edge (strut) lengths will be:

Red (A): 3' 9"
Yellow (B): 4' 4-3/4"
Brown (C): 4' 2-3/8"
Green (D): 4' 8-1/8"
Orange (E): 4' 3-7/8"
Black (F): 4' 6-7/8"
Gray (G): 4' 9"
Purple (H): 4' 11-5/8"
Blue (I): 5'

Curved 6v Dome Panel on a spherical surface.

6v Dome Panel
Flat 6v Dome Panel Diagram

### Did you notice any patterns for the strut lengths?

(Look at the total length of the struts on the outside edges of the dome panels and see if they are shorter than the total length of the struts passing through the middle of the panel.)

# How to Determine the Frequency of A Geodesic Dome.

5-way Hub Connection.
Only 6 in every dome.

### Every Geodesic Dome has only six 5-way hub connections.

#### All other connectors will be 6-way hub connections.

6-way Hub Connection.

### The Six 5-way Hub Connections represent the corners of the original Icosahedron, and the struts between each of these 5-way connections is the edge of the face of the original Icosahedron.

2v edge of the original Icosahedron face.
(2 struts)

3v edge of the original Icosahedron face.
(3 struts)

4v edge of the original Icosahedron face.
(4 struts)

5v edge of the original Icosahedron face.
(5 struts)

6v edge of the original Icosahedron face.
(6 struts)

2v Dome

3v Dome
4v Dome

5v Dome
6v Dome

# What are the Geodesic Frequencies of These Domes?

1v   2v   3v   4v   5v   6v

1v   2v   3v   4v   5v   6v

1v   2v   3v   4v   5v   6v

1v   2v   3v   4v   5v   6v

1v   2v   3v   4v   5v   6v

1v   2v   3v   4v   5v   6v