## Metal and glass geodesic greenhouses section added

May 032013

We have just added a new section, glass and metal greenhouses. For those looking for aluminum and glass geodesic dome greenhouses, Peter Ellis offers very stylish and well-built structures.

We invite you to look at the other pictures Peter has provided to us by viewing the new glass and metal greenhouse page.

Peter is also the inventor of a new type of geodesic hub. Here below is one of them. As you can see the hubs are designed to work with traditional square tubing which for many is a benefit because covering your dome is now much easier.

Peter also offers traditional domes for a variety of uses, and our favorite is how one of his domes was used by a theater troop in Ireland to put on a show for disabled kids. Not only do the actors do a great job as you can tell by the video clip below, but also the children seem to have a great time.

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Apr 052013

## More Models

So far, I have dealt with forms generated from the icosahedron and a subdivision parallel to the original icosa face sides.

This can be called the “Alternate Breakdown”. This image below from part 1 describes this breakdown resulting in higher frequencies everytime you subdivide.

There is another type of breakdown, and for this we must go back to the original icosa triangle. Instead of drawing lines parallel to the triangle’s sides, we draw lines peggendicular to them.

This is called the “Triacon Breakdown.”

2v Triacon

Icosa face shown dotted

4v Triacon

Icosa face shown dotted

There are some interesting differences between the Alternate and Triacon breakdowns. Since the triacon breakdown is symmetrical about a line drawn down the centre of the icosa triangle, the triacon is only possible in even frequencies. The alternate, however, is possible in all frequencies. In even frequency alternate breakdowns (2v, 4v, 6v) great circles are formed which divide the sphere neatly into hemispheres.

The triacon breakdown does not have this feature in any frequency. ln order to make a triacon half-sphere. some triangles have to be cut in half. The triacon requires fewer different lengths because of  its higher symmetry, but. on the other hand. the struts vary in length more than in the altemate breakdown.

Try a model and see the differences.

To make a 4v triacon sphere you will need:

By now you should ?nd it fairly easy to identify different types of domes. What you do is look for a point where ?ve struts join. Then ?nd another pentagon and draw a line between them. If this line is de?ned by actual struts. then the dome is an altemate breakdown. If there are no stmts along the line. the dome is a triacon. What you are doing is picking out comers of the original icosa. The line you draw between them is an icosa edge. and counting the number of parts into which it is divided gives you the frequency of the dome.

Domes can also be generated from the Octahedron. They are not as round as domes generated from the icosahedron and can be easily recognised by a square where the eight octa faces meet. The Octahedron form has the distinguishing ability to be able to fuse to rectilinear forms. The Octahedron also forms a natural truncation at the hemisphere.

Assembly methods are as follows:

Domes can also be squashed or stretched to give an ellipsoidal form.

These forms are useful if building big domes where the dome is squashed down to save both headroom and surface area.

THREE FREQUENCY ICOSAHEDRON ELLIPSOID (SQUASHED)

One last word on model making is to make paper or cardboard models. Use the patterns on the following pages. Punch with a pin through the paper onto thin cardboard. or trace onto paper.

Trace ?ve times for the Icosahedron based domes, four times for the Octahedron based domes. Either tape the gathering angles to form curved sections or add tabs on the edges which can be glued or stapled together inside. Very attractive scale models can be made by using artist’s mount board and gluing the edges together on the insides with a hot glue gun.

In calculating dimensions. the following formulas are useful:

π = 114159265

CIRCUMFERENCE OF A CIRCLE = 2 * π *R

AREA or A CIRCLE = π * R²

AREA or A SPHERE =4 * π * R²

VOLUME OF A SPHERE = 4/3 * π * R³

AREA OF A TRIANGLE = 1/2 * BH

4v ICOSA ALTERNATE

3v ICOSA ALTERNATE 5/8 SPHERE (MAKE 5)

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Apr 032013

# MODEL MAKING

By far the best way to see what a geodesic dome looks like is to build three dimensional models. This is not difficult and lets you see how the geometry works, what size and shape you like and possible window and door placements.

The best drawings and photos are inferior to the simplest model when it comes to demonstrating three dimensional relationships.

Playing with models can lead to the discovery of valuable insights; not to mention that they are fun to make and look beautiful too.

There are two basic types of model building, as is full scale dome building. These are:

1. The HUB AND STRUT method. ie. Building a framework and then covering it with a skin. and
2. The MEMBRANE or PANEL system. ie. Where the skin is attached to the struts in premade triangular panels and the panels are later bolted together.

Before starting your first model, there are a few more simple geometric elements to become familiar with. These are:

CHORD FACTORS, CENTRAL ANGLES, AXIAL ANGLES,

FACE ANGLES and DIHEDRAL ANGLES

For each type of dome there is a method of calculating strut lengths and the angles at which they meet and how they are assembled.

The CHORD FACTORS are of the most importance here as they are needed to determine strut lengths.

Chord Factor = 2 Sin (Central Angle/2)

STRUT LENGTH = DOME_ RADIUS X CHORD FACTOR

Once you have a table of chord factors you can calculate strut length for any size dome you want.

The CENTRAL ANGLE is the angle produced by extending a line from the strut ends to the centre of the sphere.

AXIAL ANGLES are useful in hub design. They are the angles that the strut ends make with the centre of the sphere.

Axial Angle =  180 degrees minus Central Angle /2

FACE ANGLES are the internal tip angles of the triangles and are necessary when cutting hubs and triangle panels.

DIHEDRAL ANGLES are the angles between triangles. They are useful if you plan to bevel the skin panels or use bevelled struts.

2v and 3v breakdowns with original Icosa face dotted

The diagram above shows the statistics for a Three Frequency Icosahedron Dome.  To make a 5/8 sphere you will need:

Choose your method of model assembly (following pages) and assemble as in the diagram on page 8. This model will sit ?at on the 3/8 and 5/8 levels. It is simpler to join all the pentagon and hexagon spokes together ?rst. Make six pentagons from “A” struts, ten hexagons from “C” struts and ?ve “halt” hexagons for the base.

A simpler model can be made using only three strut lengths by substituting “D” struts with “B” struts and using the new chord factors of:

A = .34862       need 30
B = .40355       need 55
C = .41241        need 80

This model will not sit flat however but will rest on the five half-hex hubs under the pentagons. For a very similar truncation (fraction of a dome), the Kruschke method is used (in this case a 5/9).

## Three-frequency icosahedron spheroid

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## The Geodesic dome DIY Handbook Part 1

Apr 022013

INTRODUCTION

This e-booklet has been compiled to assist potential owner-builders of Geodesic Domes to prefabricate and erect a variety of geometric configurations utilising a number of possible construction techniques.

Much of the data is gleaned from long-out-of-date publications and from the author’s practical experience and experimentation in building domes since 1973.

Most of the ideas within have been tested and proven successful but are certainly open to further refinement and development. Rather than promoting any one system as being the ‘best’, I would prefer to offer ideas and possibilities to the great Australian tradition of “Do-it -yourself” and share my own experiences of what can work.

With this in mind I welcome any feedback about your own experiments, learning experiences and successes and invite any correspondence to share such knowledge. This manual is intended for educational purposes only.

It presents information on principles and techniques that the author has not necessarily employed. It is not suggested that these methods must be followed or that if followed will result in a safe or satisfactory building.

Due to variations in materials, quality of workmanship, tools and equipment, materials and components, local building codes etc., the author assumes no liability for any structure designed or constructed from information in this manual unless it is built by The Dome Company or our nominated sub-contractor.

# Geodesic Geometry

GEODESIC = The shortest line between two points on a sphere.

There are only five different structures that we can build where all the sides, faces and angles are equal. These regular solids are called PLATONIC solids.

Of these five, we see that three are made of triangles. As we might expect, the tetrahedron,octahedron and icosahedron are rigid; while the cube and dodecahedron are not. The cube is the basis for most types of buildings. The icosahedron is the basis for most Geodesic Domes.

You can make small structures with icosahedrons, but if you begin to make bigger structures, the triangles get large and heavy and you begin to need big timbers for the members.

Dome geometry is all about the subdivision of large triangles into smaller ones.

An Icosahedron has twenty equilateral triangular ‘faces’. When the face is subdivided. it is not
done equally, but done so that the faces begin to curve outward;this gives you more strength. Each face can be divided by a line (arcs on a sphere) parrallel to the edge.

The number of divisions is called “FREQUENCY”.

As the frequency increases, the number of members or “STRUTS” and the numbel of triangles increases also, and the closer you get to a sphere.

The following diagram below is of a THREE FREQUENCY (3v) ICOSA 5/8 SPHERE.

Each of the original Icosa faces is heavily outlined. Looking at a geodesic dome on can determine the frequency by counting the number of struts between the apexes 0f the pentagons.

Note: divisions are different for different frequencies. See chart below for correct nomenclature

Consider the domes outlined below

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## Geodesic Plans Collection

Mar 292013

If you are looking for geodesic plans for a greenhouse, shed, or just a nice summer patio, be sure to look at the new Geodesic Plans page.

These plans are offered by Paul of Geo-dome and all plans include support to help you build any of the structures offered. Prices vary between \$24 and \$45. All plans have been built and tested.

Best of all, these are hubless designs which require a minimum of tools to make.

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