Geodesic dome bevel angle

[owen s]

Lets say that I am using a 4v geodesic dome and I have the length and angles of the wood from a geodesic dome calculator like this one: http://geo-dome.co.uk/4v_tool.asp

If I want to make the frame without hubs and struts but instead use something like this: 

Where each triangle is screwed together, then they are assembled.

There needs to be a bevel angle so that the dome will pop up and form properly.

How do I calculate the angle to bevel each piece of wood that would be used to assemble the frame?

Say for example from an image like this:

More images

[Gerry in Quebec]

Owen,

If you use the triangular panel construction method described at www.geo-dome.co.uk, then the bevel angle for ripping struts on a table saw is half the difference between 180 degrees and the dihedral angle.

 

So, bevel angle = (180 - dihedral angle) / 2.

Cheers,

- Gerry in Québec

[owen s]

Thank you Gerry

I will be attempting this project shortly. 

[owen s]

I started creating a test with some foamcore but I just realized an issue.

I wanted to build the frame without using hubs but the dome calculator doesn't show the internal angles for the 4v model.

how do I bevel the edges of the struts to get them to align as in the image

based on the 4v angles?

[Gerry in Quebec]

Owen,

If you want to know how to bevel the ENDS of the struts (rather than the faces of the struts, lengthwise), you subtract the internal (i.e, face) angle from 90 degrees. That's the tilt angle of the saw blade -- for example, on a compound mitre saw. The attached drawing gives the internal (face) angles for the 4v icosa dome, so-called class I, method 1, which is the same geometry used by Geo-Dome's 4v calculator.

Note: That calculator gives you the edge lengths of the component triangles. Because the panel dome construction method you've chosen uses butted joints, the edges of the triangles are longer than the actual struts. Before attempting to build even a model, you might want to view Pauly Robinson's YouTube videos, starting with one from around 2011, titled "geo-dome plans intro":

https://www.youtube.com/watch?v=U32KTMtp5kU&t=198s

Good luck,

- Gerry in Québec

[Gerry in Quebec]

Owen,

The bevel cuts I mentioned in my previous post refer to the ends of the three struts that form the triangular jig. That jig, or pattern, is then used to cut and assemble the struts that form the triangular dome panels. By using the jigs, you don't have to calculate any compound angles.

- Gerry in Québec

[Paul Kranz]

Owen, another way, if the triangles are small enough, is to bevel them after you construct them. It worked with a 2v icosa. Paul sends...

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[stongeQc]

Hey Im looing to build a 2v beveld dome and I am trying to figure out de dihedral and the bevel angles. befor seeing your post GErry in Quebec, I think that the bevel angle and the dihedral angle were the same thing!? I found that 11 degrees for one side and 7 degree for other side. does that mean I need to cut each piece of wood by either 11/2 or 7/2? and then assembled it will make the 11 and 7 angles?

Thank you for the help

MAt

[Dick Fischbeck]

Consider building a random and forget the trigonometry.

[Levente Likhanecz]

hi stongeQc,

there is a rather old technique to "measure" the bevel angles.
steps:
1. decide dome radius for you 2v
2. strut lengths will come from your calculator.
3. cut out 2 sample triangle (AAB and BBB) from plywood or chipboard.
4. go on a flat floor where you have enough space for your radius.
5. stick a nail into the floor (or whatever fix point) attach a
measuring tape's zero end to it.
6. strech the tape to your radius, and fix 1 tip of the triangle
(standing 1 edge flat on floor), (mark the position with a marker for
ease)
7. align the the other tip sitting on the floor to be on radius. (the
previous tip stays on the mark)
8. when both floor-sitting tips on radius, lean the triangle's top tip
toward the nail, till also on radius. just lean it onto a box or
chair.
9. recheck all three tips on radius distance from center nail.
10. your bevel angle of the bottom edge now measurable between the
floor and the triangle's plane.

repeat it with all sides of both triangles

later on if you decide higher V domes that method works same.

cheers, lev

On 10/4/20, stongeQc <stong...@gmail.com> wrote:
> Hey Im looing to build a 2v beveld dome and I am trying to figure out de
> dihedral and the bevel angles. befor seeing your post GErry in Quebec, I
> think that the bevel angle and the dihedral angle were the same thing!? I
> found that 11 degrees for one side and 7 degree for other side. does that
> mean I need to cut each piece of wood by either 11/2 or 7/2? and then
> assembled it will make the 11 and 7 angles?
> Thank you for the help
> MAt
>
> Le mardi 25 décembre 2018 à 07 h 45 min 42 s UTC-5, Gerry in Quebec a
> écrit :
>
>> Owen,
>>
>> If you use the triangular panel construction method described at
>> www.geo-dome.co.uk, then the bevel angle for ripping struts on a table
>> saw is half the difference between 180 degrees and the dihedral angle.
>>
>>
>>
>> So, bevel angle = (180 - dihedral angle) / 2.
>>
>> Cheers,
>>
>> - Gerry in Québec
>>
>> On Tuesday, December 25, 2018 at 6:28:36 AM UTC-5, owen s wrote:
>>>
>>> Lets say that I am using a 4v geodesic dome and I have the length and
>>> angles of the wood from a geodesic dome calculator like this one:
>>> http://geo-dome.co.uk/4v_tool.asp
>>>
>>> If I want to make the frame without hubs and struts but instead use
>>> something like this:
>>>
>>>

>>> <http://control-zeta.org/wp-content/uploads/2014/10/Geodesica-Sin-nudos-Completas-2.jpg>

>>>
>>>
>>> Where each triangle is screwed together, then they are assembled.
>>>
>>> There needs to be a bevel angle so that the dome will pop up and form
>>> properly.
>>>
>>> How do I calculate the angle to bevel each piece of wood that would be
>>> used to assemble the frame?
>>>
>>> Say for example from an image like this:
>>>

>>> <http://geo-dome.co.uk/photos/4vdihedrals.jpg>
>>>
>>>
>>> More images
>>>
>>> <http://geo-dome.co.uk/photos/4v_calc_panels.jpg>

>>>
>>>
>
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[Levente Likhanecz]

something wrong with the attachment
of method

[Gerry in Quebec]

Hi Stonge-QC,

For a 2v icosahedral dome, the edge bevel angle of the shorter edges (chord factor 0.546533) in the icosceles triangles (smaller of the two types of triangles) is 11.2 degrees. For the longer edges (chord factor 0.618034) in that type of triangle, the angle is 7.2 degrees. For all three edges (chord factor 0.618034) in the equilateral (larger) triangles, the edge bevel angle is 10.8 degrees.

 

These are the angles you get when all calculations are referenced to the spherical centre of the geodesic sphere.

The dihedral angle you mentioned is the angle between two faces of a geodesic dome. See the attached diagram. The edge bevel angle of edge AC in triangle ABC is 90 degrees minus"partial" dihedral angle EKN. The edge bevel angle of edge AC in triangle ADC is 90 degrees minus partial dihedral angle HKO. The dihedral angle between triangles ABC and ADC is angle EKN plus angle HKO. 

To build a small dome with lumber, maybe you can just use 11 degrees for all the cuts. I don't know. Paul Kranz and Paul Robinson have experience making such triangular frames, so maybe he can suggest whether "one angle fits all" or not.

Your moniker suggests you're a fellow Québecois. I live in the Outaouais Region, north of Ottawa-Gatineau.

Salut,

- Gerry in Québec

[Adam Winter]

Hi MAt,

You mean something like this?:  https://patents.google.com/patent/US9506240B1/en

It's a function of the angle between the two struts and the angle between each strut and a vector that is orthogonal to the component vectors of all the struts, at that hub, that are in the same plane.  In other words, if you look at one hub/node and think of the struts extending from there as the ribs of an umbrella, then the handle of the umbrella is a vector that is (approximately) no closer to any rib than another.  I've seen that angle referred to as the "drop angle" and that's what I like to call it.  That is, if your umbrella were perfectly flat, instead of dome shaped, then the umbrella handle would be orthogonal to all the ribs;  each rib would be at a 90-degree angle with the handle.  Instead each rib/strut "drops" below 90 degrees, and how much less than 90 degrees is the "drop angle".

Now, with icosahedral domes, the struts at any given node drop at differing angles.  This is why the nail-and-board approximation is only an approximation.  Trying to make triangle frames this way is very difficult.  Furthermore, with icosahedral domes, because each hub/node has multiple drop angles, each triangle frame has three different drop angles, and you have to keep track of which is which.  This is one of the main advantages of the dome I linked to in the patent above.  

I've been meaning to put together a web calculator that gives you the bevel setting on your saw, given the interior angle of the triangle and the drop angle. 

Adam Winter

The Bootstrap Music Co.

206-430-4425

ad...@bootstrapmusic.com

www.bootstrapmusic.com

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[Gerry in Quebec]

Here's a link to a related discussion in February 2015.

https://groups.google.com/d/topic/geodesichelp/uT4EA-V6768/discussion

On Sunday, October 4, 2020 at 2:30:03 PM UTC-4, stongeQc wrote:

[stongeQc]

Oh yeah thanks guys!

Thanks for the knowledge Gerry It is now clear what my angle are going to be. 

Gerry oui je suis du quebec aussi mais de l'autre bord, de Rimouski hehe.

And for the fun of understanding the maths behind the 7.2 the 11.2 and 10.8. Gerry do you have a formula that gives these angles, like using the radius of the sphere and de 2v icosahedron form..?

MAt

[Gerry in Quebec]

Hi MAt,

There are several ways to calculate dihedral angles and related bevel angles. I'll look through my Excel files to find the simplest math expression of these, and post it soon. I may already have done so a few years ago, in which case you might want to try the Search conversations function on this Google group using the words "dihedral angle". 

Happy Canadian Thanksgiving!

- Gerry in Québec

[Gerry in Quebec]

Hi MAt,

The attached image gives the equation for the dihedral angle between triangular faces of a geodesic dome or sphere. It assumes that all vertices are the same distance from the spherical centre. You may also want to look at the following discussion, which contains an Excel spreadsheet that gives equations and calculates the partial dihedral angle for geodesic domes:

https://groups.google.com/d/topic/geodesichelp/a5upLyCT8f4/discussion

Cheers,

- Gerry in Québec

[Gerry in Quebec]

Hi again MAt,

My last message contained the wrong png image, one I had already posted. Here is the one I meant to post.

- Gerry in Québec

[Cindi]

Adam a calculator would be fabulous!   I will be building a 4V4S x 3 with a central dome 6V9S  This is the Sketch up link Lev did and all the calculations too :)
https://3dwarehouse.sketchup.com/model/ebc4edcf-4e85-480c-870e-7d4507545e51/6V9S-to-4V4S-clusterable-flat-seaters?login=true#

Cindi

[Levente Likhanecz]

https://3dwarehouse.sketchup.com/model/16ed2509-1606-405c-b524-d84a2dc18e6b/6v9s-and-4v4s-resize-pair

>> 206-430-4425 <(206)%20430-4425>

>>>>>> <http://control-zeta.org/wp-content/uploads/2014/10/Geodesica-Sin-nudos-Completas-2.jpg>

>>>>>>
>>>>>>
>>>>>> Where each triangle is screwed together, then they are assembled.
>>>>>>
>>>>>> There needs to be a bevel angle so that the dome will pop up and form
>>>>>>
>>>>>> properly.
>>>>>>
>>>>>> How do I calculate the angle to bevel each piece of wood that would be
>>>>>>
>>>>>> used to assemble the frame?
>>>>>>
>>>>>> Say for example from an image like this:
>>>>>>

>>>>>> <http://geo-dome.co.uk/photos/4vdihedrals.jpg>
>>>>>>
>>>>>>
>>>>>> More images
>>>>>>
>>>>>> <http://geo-dome.co.uk/photos/4v_calc_panels.jpg>
>>>>>>

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[Pedro Valle]

Hi.i want to build something to like these ..I need 3D design to make the molds to do it with aircrete .. thanks in advance

To view this discussion on the web visit https://groups.google.com/d/msgid/geodesichelp/CAOkvED%3DHBeMgUcgFSp6fxA-n%2BVO4HgCU6uEdZA%3DUSYi9aOcO6g%40mail.gmail.com.

[valle....@gmail.com]

Hi. Rob thanks for fast reply....   30 ft diameter and 8 inches thick walls ... I use pepakura to create papers molds and to make them hard, I paint them with resin or varnish .. I own a Roland vinil cutter ... So I can remove the knife and put a pen ...is 24 inches wide ... 

Sent from Yahoo Mail on Android

On Fri, Dec 4, 2020 at 12:16 PM, clark.rob...@gmail.com

<clark.rob...@gmail.com> wrote:

What diameter dome do you want to build?  What thickness of walls?  How will you be creating molds from the 3D models?  

https://groups.google.com/d/msgid/geodesichelp/c112c5cf-7ba4-47c3-8f0c-7058db353a0an%40googlegroups.com

.

[Pedro Valle]

Rob .. thanks a lot ..just what I was looking for. Is perfect just need make 2 . One bigger with 8 inches  in diameter ... Center both ..and then separate the shapes from exagonos and pentagons ..and from there I can export the files on dxf or obj .. import them in pepakura and print the shapes in my plotter ..I'm no working these weekend I will try to post some pics .. thank you again ... 

On Fri, Dec 4, 2020, 2:12 PM clark.rob...@gmail.com <clark.rob...@gmail.com> wrote:

I've tried to respond a couple times now, but anytime I paste an image the page crashes.  With the new format, I no longer see any button for uploading an image off my hard drive.

Anyway, I'll try pasting a link to a SketchUp model that is of the dome shape you are looking for.  It is called a C960 Fullerene.  This is the link:

https://3dwarehouse.sketchup.com/model/8d844ae2415824c0c901553684b98881/Icosahedral-System-Equal-Central-Angle

To view this discussion on the web visit https://groups.google.com/d/msgid/geodesichelp/3080cb4e-b097-4dcb-832c-dfea798bd282n%40googlegroups.com.

[Gerry in Quebec]

Hi Pedro & Rob,

The SketchUp models by Taff to which Rob posted a link are based on Clinton's Equal Central Angle Conjecture. The hexagons in all but the simplest of these structures are not flat; so there could be problems constructing aircrete panels and making them fit together. 

Here's a link to an earlier Geodesic Help conversation about the hex-pent dome/sphere in question, namely Goldberg polyhedron I {3,3}:

https://groups.google.com/g/geodesichelp/c/hvRPHGNKxiY/m/tafZ6jOiCQAJ

This structure is a true polyhedron, i.e., with flat faces. It's based on the dual of a 6 frequency, class I geodesic sphere generated by Antiprism's pol_recip program.

The relevant discussion, which overlaps with a discussion of I {2,2}, starts on Feb. 3, 2016. I also posted a simple SketchUp model of the 12/27 truncation of I{3,3}, on Feb. 8. The bottom row of hexes and half-hexes was doctored to make the dome sit flat.

- Gerry in Québec

On Friday, December 4, 2020 at 6:12:44 PM UTC-5 clark.rob...@gmail.com wrote:

I've tried to respond a couple times now, but anytime I paste an image the page crashes.  With the new format, I no longer see any button for uploading an image off my hard drive.

Anyway, I'll try pasting a link to a SketchUp model that is of the dome shape you are looking for.  It is called a C960 Fullerene.  This is the link:

https://3dwarehouse.sketchup.com/model/8d844ae2415824c0c901553684b98881/Icosahedral-System-Equal-Central-Angle

On Friday, December 4, 2020 at 4:33:44 PM UTC-5 valle....@gmail.com wrote:

[Gerry Toomey]

Re: Geodesic dome bevel angle  

Just testing to see if I can post an attachment by responding by email to geodes...@google.groups.com with the correct conversation name.

Attempted attachment is a png screenshot of a SketchUp model of the I{3,3} hex-pent sphere.

- Gerry in Québec

On Sat, Dec 5, 2020 at 9:43 AM clark.rob...@gmail.com <clark.rob...@gmail.com> wrote:

I could be more helpful if I could paste images or post attachments.  The paperclip symbol in the menu bar no longer appears.  I take this to mean my permissions to post attachments have been removed.  Not sure why.  This does not inspire me to continue to participate or contribute.

Robert

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[Gerry in Quebec]

On Saturday, December 5, 2020 at 9:36:46 AM UTC-5 Gerry in Quebec wrote:

...This structure is a true polyhedron, i.e., with flat faces. It's based on the dual of a 6 frequency, class I geodesic sphere generated by Antiprism's pol_recip program.

That should read, "...dual of a 6 frequency, class II geodesic sphere..."

 - Gerry in Québec 

[Levente Likhanecz]

hi Pedro,
somewhere, someone attached a png pic of a (3,3) hexa-dome.
i drawn such a dome in sketchup based on Chris Kitrick's calculations.
all hexagons and the pentagon is flat, and the tips (vertices) sit on
the sphere.
if you wanna check is here:
https://3dwarehouse.sketchup.com/model/800b4604-e846-4d3c-a3e8-427c11f0e32e/hexagon-dome
please note the backside of the 5 building elements completely flat.

On 12/5/20, Pedro Valle <valle....@gmail.com> wrote:
> Rob .. thanks a lot ..just what I was looking for. Is perfect just need
> make 2 . One bigger with 8 inches in diameter ... Center both ..and then
> separate the shapes from exagonos and pentagons ..and from there I can
> export the files on dxf or obj .. import them in pepakura and print the
> shapes in my plotter ..I'm no working these weekend I will try to post some
> pics .. thank you again ...
>
> On Fri, Dec 4, 2020, 2:12 PM clark.rob...@gmail.com <
> clark.rob...@gmail.com> wrote:
>
>> I've tried to respond a couple times now, but anytime I paste an image
>> the
>> page crashes. With the new format, I no longer see any button for
>> uploading an image off my hard drive.
>> Anyway, I'll try pasting a link to a SketchUp model that is of the dome
>> shape you are looking for. It is called a C960 Fullerene. This is the
>> link:
>>
>> https://3dwarehouse.sketchup.com/model/8d844ae2415824c0c901553684b98881/Icosahedral-System-Equal-Central-Angle
>>
>> On Friday, December 4, 2020 at 4:33:44 PM UTC-5 valle....@gmail.com
>> wrote:
>>
>>> Hi. Rob thanks for fast reply.... 30 ft diameter and 8 inches thick
>>> walls ... I use pepakura to create papers molds and to make them hard, I
>>> paint them with resin or varnish .. I own a Roland vinil cutter ... So I
>>> can remove the knife and put a pen ...is 24 inches wide ...
>>>
>>>
>>> Sent from Yahoo Mail on Android

>>> <https://go.onelink.me/107872968?pid=InProduct&c=Global_Internal_YGrowth_AndroidEmailSig__AndroidUsers&af_wl=ym&af_sub1=Internal&af_sub2=Global_YGrowth&af_sub3=EmailSignature>

>>> https://groups.google.com/d/msgid/geodesichelp/CAOkvED%3DHBeMgUcgFSp6fxA-n%2BVO4HgCU6uEdZA%3DUSYi9aOcO6g%40mail.gmail.com

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[Pedro Valle]

Hi . Rob Gerry and Levente ..thank you for you help ..I'm no really good yet in sketchup ..but I'm 75 % on the proyect dome airecrate,, I will share pics and files in eps and pdf  ... Is easy but time consuming .. . 

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[Gerry in Quebec]

Hi Lev,

I had forgotten about that elegant version of the I{3,3} by Chris Kitrick, with all vertices equidistant from the centre and all faces flat. Thanks for re-posting it

- Gerry in Québec

[Levente Likhanecz]

hi Gerry,
just downloaded again from my 3d warehouse account. ( upon some anger
management issues i unfortunately destroyed my most recent rig with a
3kg sledgehammer without backup)

i'm working on the Pedro model of it 30ft dia 8" thickness.

i noticed that for some reason there are ~0.2mm differents on the
outer edges of blocks.

from sphere center i drew lines through vertices, then i pus out a
flat to 8", then the projection lines intercept the outer plane
bla-bla-bla. but outer "struts" (some) dont come same on neighbours.

should i play more, or it is normal mathematically?

cheers, lev

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[Levente Likhanecz]

hi Gerry,
i guess it is a feature not a bug, that the outer faces don't come
shoulder to shoulder.
the bigger the difference between the joining poligons in size, the
shoulder come bigger.

ok, at these sizes the grey pentagon and the yellow hexagons have the
biggest trouble, ~1mm "sink".

the inner faces aligned seamlessly on same radius.
mission impossible that all buiding panel being the same thickness.
but plaster up can help.

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[valle....@gmail.com]

Hi Levente ..  thank  a  lot for   the  file  im using old design of  Rob ,, but  i just open the last file  in sketchup ..is  pretty impresive i just converted to pepakura here one  pic .. sorry is  very confusing reply emails here and  attach files ...hope  doing it  right   

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[Levente Likhanecz]

hi Pedro,
there is an updated sketchup file attached here.
its a 30 feet diameter (inner) and the blocks are 8 inches thick.
there are some discrepancies, but for practical build seems negligible.
in sketchup you have a measuring tape tool to check for dimensions.

cheers lev

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[Levente Likhanecz]

oh, Pedro,
one important thing with the design file.
there is no allowance for mortar between the blocks to glue them together.
if you build the casting molds exactly as per design, then you have to
push out the blocks to touch bigger radius to let the panels "float
away" from each other to accomodate mortar glue.

what i mean? by the design the inner "corners" of the panels 4752mm
(15 feet) from the dome center. you have to increase the build radius,
push out all the panels (radially) till you have few millimeters
between them to accommodate the mortar.
you can check with 2 panels how much you have to push them out to have
this extra space between them, then you can use this larger radius for
all the panels.

i hope you get it.

cheers, lev

[Levente Likhanecz]

okay, Pedro,
i've checked up how much should increase the actual build radius to
have place for glue.
so by design inner corners (vertices) are sitting 4572 mm radius all,
but panels touch each other.
you increase placement by 20mm (radius = 4592 mm) then panels float
away ~3.6 mm.
on +30 mm radius (4602mm) distance between panels (grout) ~5.4mm

so each centimeter increase (push out) on radius result ~1.8mm growth
mortar place between panels. like you lay ceramic tiles on floor with
those plastic cross spacer pieces.

cheers, lev

On 12/9/20, valle....@gmail.com <valle....@gmail.com> wrote:

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[Gerry in Quebec]

Hi Lev,

For all panels to have a uniform thickness when the radius to all outer vertices is constant (15' in this case), the radius to the inner vertices of one hex panel will differ from the radius to the inner vertices of other panels.

- Gerry

[Levente Likhanecz]

thanx Gerry,
i arrived to the same conclusion after some struggling.
only i approach from inner to out, thinking build-wise.
(you know, to stick a dome centerpoint into the ground, and a single
string - radius- the building-aid to set panel vertices).

practically ~1mm misalignment at 30ft/8" i would not care any more to
avoid headache.
can smear some mortar to cover up geometry mayhem.

meanwhile in private msg from Pedro i advised to cast panels as per
design dimensions, but inrease build radius to allow mortar / glue
between panels. (1cm increase in radius makes 1.8mm space between
panels)

cheers, lev

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