Design

Geometery

The ‘Hexagon’ dome design is based on a
Class II polyhedra, Icosahedral (Goldberg).

https://en.wikipedia.org/wiki/Goldberg_polyhedron

The geometry is based on a 3v frequency or GP(3,3) notation, with just over a half sphere to result in a pattern that allows for minimal face variations and an eye pleasing symmetry.

The internal height is a minimum of half the dome diameter, but generally around 60% of the diameter in these designs, and around 80% in the `bubble` style dome.

Specific Internal heights can be referenced on the table further down.

The Geometry repeats 5 times around the central Pentagon, with a similar pattern to the one shown here.

The door and bottom faces, are trimmed down versions of the full faces.

The Frequency, Diameter and sheet material size considerations

The dome frequency affects the number of faces.
The diameter affects the size of the faces
The sheet material affects how many faces per sheet can be cut
The sheet material flexibiltiy affects how large or small the sheets can be.

A 3 frequency or GP(3,3) Geodesic half sphere dome based of a Goldberg Polyhedron, requires 166 faces, of 6 different face types.

In a 4m design, the largest of these piece is 560mm x 560mm.

Sheet material can be sourced upto 1200mm x 2400mm, which can neatly fit 8 faces per sheet with a minimal amount of waste.

To cut 166 faces, this will require 20 sheets.

If you are looking for higher frequency or larger diameter, there are some restrictions....

3 Frequency 10m diameter dome will require faces over 1200mm, and will not fit most regular sheet material sizes.
4 Frequency for 10m diameter requires faces upto 1000mm, this will limit the layout to only 1 face per sheet. The geometery uses 241 panels, of 10 different type requiring 241 sheets.
6 Frequency for 10m diameter requires faces upto 600mm, with a total of 541 faces, of 20 different types. 8 faces can be produced per sheet, requiring 68 sheets and a very complex construction.

There are many variations that are possible, my Etsy shop lists some of the common sizes, a bespoke design can be discussed if required.

Dome Freq Calculations

Costs & Quantities

A common question is how much will a dome build cost? , to assist with the variety of domes and breakdown of the associated costs, the table below provides some initial calculations. There are many varying factors, the biggest being the material costs and CNC cutting.

If you can source cheap materials, even secondhand sourced for a fraction of the retail price for new, then you dome build will be significantly more affordable.

And if you fabricate the faces yourself, you save again.

As you can see from the table below, based on the 3 fequency Goldberg Polyhedron, the 4m diameter is a good size - and if your going to make 6m - you might as well make 7m for the same price with less waste.

IMPORTANT NOTE : these estimated sheet sizes are based on ALL faces being the max size, in reality this is not the case and more faces may be able to be cut from 1 sheet where the faces are smaller. These are approximate numbers and you will need to calculate your own quantities based on the fabrication method, material size and face layour per sheet.

Dome Calculations

Material Choice

Polycarbonate or Acrylic ?

Both offer different properties and may depend a lot on the availablity, sheet size, how you are planning to cut the sheet and the cost in your area.

Both acrylic and polycarbonate are weather resistant and expand and contract with temperature changes without long-term or permanent shrinkage.

Polycarbonate

is shatterproof
can scratch as the surface is softer
is the stronger material - and this is reflected in its common applications as an all-weather glazing material and as bulletproof 'glass'.
is slightly more durable than acrylic and less likely to crack under stress
low flamability
lets slightly less natural light through at 88%
is often treated to be UV-resistant , but can be UV permeable

Acrylic

is typically a more rigid plastic
is shatterproof
can `chip` but it less prone to scratches
Does not yellow overtime
is flammable, but burns slowly
lets more light through with a transmission rate of 92%
if mostly UV-resistant
can be sourced as `recycled`

With this in mind, it seems sensible that acrylic is the go-to material for secondary glazing, while polycarbonate is more commonly used for roofs of structures such as bus shelters and conservatories due to its durability.

Sheet materials also come in a variety of finishes with reflective coatings, opaque and solid colours.

Its worth remembering, that once the dome is built, panels CAN be swapped out individually later on, allowing for modifications, replacements and repairs - as well as the capability to completely dismantle and rebuild in a new location.

What thickness ?

3mm or 4mm sheet material provides a compromise between cheaper more flexible sheet, vs a stronger and more durable structure.
you may choose to use 1mm polycarbonate for a super flexible dome, or 5mm acrylic for a storm proof shelter... but for thicker materials the note about flexibility above should be considered .

The thickness will also affect the natural airgap as mentioned below.

If you are planning on windows and a door frame, you material thickness will affect some of these choices, if its too thin the window will need additional support and the door frame may need additional supports.

Weight needs to be considered in your design.

As an example:

a single `Pentagon` piece of the 4m dome, in 4mm Acrylic weighs 970g.
A full dome will require 166 * ~970g, which equates to ~161Kg.

Large Domes

If you are planning to build 7m, it may be worth considering thicker 4mm sheet on the lower sections and thinner 3mm sheet on the middle and above. This will not only reduce the weight of the overall structure, but will reduce the costs.

CNC vs Hand cutting

We receive many inquiries about how to cut the sheet and if we can also supply the design as a `kit`.

Our designs were initially produced for DIY homebuilding, using hand cutting techniques with Circular saw and drills.

We would encourage the use of CNC cut templates as the base to cut and drill all the faces from, to ensure the precision and accuracy on each - as the holes need to align with a 0.5mm tolerance. With only 6 templates required for the 3 Frequency dome, this is not a significant cost as it will reduce waste and errors in fabrication and speed up the process.

If you choose to CNC cut ALL the pieces, you will end up with a very accurate and professional finish.. It may be worth looking to purchase your own CNC cutting tool (eg www.Ooznest.co.uk) as the initial cost of the machine will pay for itself in the speed and accuracy once setup and could be resold at 60-80% value once completed. A machine will need the table size of the largest face for the dome you want to build - be sure to check before purchasing.

Unless you have a full size CNC routing table capable of 1.2 x 2.4m sheet, you will probably need to cut down the larger sheets into smaller sections for the CNC router.

Alternatively, there are many smaller woodworking workshops around that would happily do the CNC cutting for you, or even Waterjet and Laserjet. They do come at a price but leave you with cut parts ready to bolt together and no mess from the fabrication.

This is a convenient option, but does mean you will need to provide all shapes for doors, front porch, windows etc upfront and may need a lot of checks to ensure you know what you are requesting as it could be costly if there are mistakes.

The CAD drawings for the parts are provided in DXF format, with one file containing multiple pages, with one page per part.

Some clients have requested individuals files per part - this can be provided if required.

If you need different formats, please contact us to inquire.

We have found that some laser cutters use SVG format. Whilst we cannot export in SVG, the, we can export STL and this can be converted for free using the `TinkerCad` website to SVG format if required.

The Drawings are provided by default as DXF and PDF, but can also be provided in other formats as below...

Drawing 1.dwg
Drawing 1.dwt
Drawing 1.dxf
Drawing 1.jpeg
Drawing 1.pdf
Drawing 1.png
Drawing 1.svg

DXF files can be viewed in various free online sites such as...
https://www.dwgsee.com/online_viewer.html

Nest&Cut

I was recently introduced to this website... (thanks to Arvid Larsson)

https://nestandcut.com/

where a range of DWF drwing parts can be uploaded , quantities set, and the full parts list optimized for any sheet layout as required.

it does a pretty good job and consolidated the cut layout over 20 sheet of 2400x1200mm, for the 5m dome plans. (this was the 5m dome, with 2 extra windows and no door plans).

Overlapping Panels & Construction

The Dome designs using overlapping sheet panels with the top panel overlapping the lower, direct rain water over the outside preventing water ingress into the dome.

On a 3 Frequency dome, each panel is around 10 degrees offset from its neighbour. With the correct thickness and flexibility on the sheet material, this offset can be accommodated by the face material flexing over its width, allowing the faces to meet on the same horizontal plane.

Sheet material choice should be checked to ensure that the material can flex the required amount over the face size to reduce stress on the structure and pressure on the fixings.

Over the structure, there are joints where 3 faces meet. There will be one face on top, a face on the bottom and one in the middle. In some occurrences (1 edge per face) the top and bottom panel will have a gap between. This could be a full width gap along the edge, or closed on one side and a gap on the other end. This is a natural by-product of the overlapping panel design. The equal size gap can be filled by using a shim of the same sheet material to fill the small thin gap and trapped in place using the existing bolts. The angular gap is not so simple to fill, and as in most cases the dome does not need to be airtight, a small air gap does allow condensation and ventilation without causing any significant draft so is best left open.

The dome structure needs to sit on a level surface so that the first base circle is perfectly round. Any skew on the first layer will cause the hole alignment to be offset further as the dome is built upwards - to a point where the holes will not meet as the structure is not aligned.

The dome is constructed from the Ground level, building upwards, with each additional face added above, overlapping the lower panel on the outside. Working around the dome building up each layer following the geometric design. It is advisable to have at least 2 people building the dome once above waist height as reaching both the nut AND bolt can be a challenge. Whilst building the dome, the nuts and bolts should be left 3/4 tightened, not fully tight - to allow the structure to settle and flex slightly as the new faces are attached and secured.

As the dome construction reaches the top, a ladder may be required to allow access from inside to the top section. Before the final Pentagon is fixed to the top, the doorway entrance will need to created and the ladder can be moved to this area to complete the final stages.

Terminology

Goldberg Polyhedron - convex polyhedron made from hexagons and pentagons.

Face - each face is either a pentagon or hexagon and join together to build the dome.

Frequency - The Higher the frequency, the more complex the geometry is and the more faces there are, but the shape becomes less angular.

Diameter - width from one edge of the dome to the opposite side.

Sheet - a flat sheet of source material. These can generally be sourced upto 1200mm (4ft) x 2400mm (8ft).

CNC - Computer Numerical Controlled, meaning computer controlled Router, Laser or Waterjet cutting. Used for precision, accurancy, repeatability and speed. - but at a cost.

Links

Want to see some Dome Photos .. CreativProjects - Photos .

Want to buy the plans to build a 3m, or upto 7m frameleess Geodesic Dome, see options here on Etsy. : CreativProjects - Etsy UK

If you are looking for traditional Frame dome constructions, check out Trillium Domes

Plastic Dome, hypedome, viking dome, geodome

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