Truncated Icosahedron

[William Fisher]

Can anyone tell me if the math here is correct. http://lumberjocks.com/rance/blog/26130

[Hector Alfredo Hernández Hdez.]

I dont see anything wrong. :)

2015-01-17 6:28 GMT-07:00 William Fisher <fisher...@gmail.com>:

Can anyone tell me if the math here is correct. http://lumberjocks.com/rance/blog/26130

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[Gerry in Quebec]

There's more than one way to skin a cat, carve a pumpkin, or split the dihedral angles of a Buckyball (truncated icosahedron). Here are three scenarios, including the one referenced by Bill Fisher, in which the dihedral angle between a pentagon and a hexagon are split evenly between the two faces. See the attached jpg.

Scenario 1: The dihedral angle between a pentagon face and a hexagon face is split so that all outer-to-inner edges of the panels align with the centre point of the Buckyball. With this arrangement, both the inner and outer faces of the hex panels are the same shape, namely regular hexagons, but the inner faces are smaller than the outer. The same goes for the pentagons. The edges of the pentagons have a bevel angle of 16.5 degrees and the hex edges 20.9 degrees. These are the angles I posted in a series of jpgs a few weeks ago.

Scenario 2: The dihedral angle between a pentagon face and a hexagon face is split evenly, as in the example given by Bill (http://lumberjocks.com/rance/blog/26130). In this case, the inner and outer faces of each pentagon are, as in scenario 1, the same shape. However, the inner and outer faces of the hexagons are NOT the same shape. The inner faces are no longer perfectly regular hexagons. In this instance, the pentagon edges and three of the six hexagon edges have a bevel angle of 18.7 degrees. The remaining 3 edges of the hexagons (where two hexagons meet) have a bevel angle of 20.9 degrees.

Scenario 3: The dihedral angle between a pentagon face and a hexagon face is split unevenly, in such a way that no beveling of the pentagon panel edges is required (bevel angle = 0 degrees). As for the hex panels, the three edges connecting to pentagon panels have a bevel angle of 37.4 degrees, and the other three edges have a bevel angle of 20.9 degrees. As in scenario 2, the inner and outer faces of the hex panels are NOT the same shape.

While the three blue models in the jpg look alike, each varies a little from the other. All three scenarios yield a buildable panelized Buckyball, but the first scenario is probably the simplest because the inner hex faces are the same, regular shape as the outer faces.

- Gerry in Quebec

On Saturday, January 17, 2015 at 10:03:26 PM UTC-5, Hector Alfredo Hernández Hdez. wrote:

[William Fisher]

Very interesting, never considered how the bevels would change the inside shape.

How would you bevel flat panels, pease method or the Oregon dome method?

[Paul Kranz]

William:

For my next dome, I will go with the Pease method. I don't like the idea of loosing all that wood with the Oregon method.

Paul sends...

On Mon, Jan 19, 2015 at 9:26 AM, William Fisher <fisher...@gmail.com> wrote:

Very interesting, never considered how the bevels would change the inside shape.

How would you bevel flat panels, pease method or the Oregon dome method?

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Very high regards,

 

Paul sends...

ReviveTheFlame.com

[Gerry in Quebec]

I have a pile of 2.5" x 2.5" spruce and cedar, about 9' long. The plan is to use this lumber for a prototype dome-like structure composed of 18 triangular panels (T-blocked frames + sheathing), using the Oregon Dome method. To avoid the wood waste Paul Kranz was referring to, I will rip each board on a table saw at the correct bevel angle to make two identical struts. (I believe this is what Paul Robinson does to make his Geodome greenhouses.) The only waste will be the sawdust and the bits at the ends of the boards.

 

A spreadsheet calculates the amount by which each edge length must be shortened to accommodate butted joints between struts. It also generates an OFF report of the triangular frame (including T-blocking), which can then be displayed in Antiview or another visualization program. The attached jpg is an example -- one of the three types of triangular frame for a 3v Fuller-Kruschke dome.

 

- Gerry

 

On Monday, January 19, 2015 at 9:44:57 AM UTC-5, Paul Kranz wrote:

William:

For my next dome, I will go with the Pease method. I don't like the idea of loosing all that wood with the Oregon method.

Paul sends...

On Mon, Jan 19, 2015 at 9:26 AM, William Fisher <fisher...@gmail.com> wrote:

Very interesting, never considered how the bevels would change the inside shape.

How would you bevel flat panels, pease method or the Oregon dome method?

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[Paul Kranz]

Gerry:

Will you be racking the triangles in a jig to construct them?

Paul sends...

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[Gerry in Quebec]

Yes, Paul, very likely.

- Gerry

[William Fisher]

Could or should I use the Oregon dome method if doing flat panel domes? I will construct hexes, pents and riser walls (the larger risers will incorporate trapezoidal tops). I was wondering how if thinning out the struts will make these weak.

[Gerry in Quebec]

Bill,

Here's a way to avoid thin struts: rip 4x4s in half at the correct bevel angles. Very little waste. See the attached jpg. You would need access to a big table saw -- probably a 12" blade. You could use 2x3s to reinforce the hex and pent panels -- some on the ceiling side and some on the roof side, as you mentioned a while back. This construction method, using the Oregon Dome approach, would make for a pretty rugged panel dome.

You mentioned that the riser walls would incorporate the trapezoids. Don't forget that the trapezoids aren't vertical.

- Gerry in Quebec

[Paul Kranz]

Bill and Gerry:

You can rip a board with a 10-in blade, but you would have to cut it from both sides.

Paul sends...

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[William Fisher]

Gerry,

I have seen plans where the riser/traps are vertical. They are reinforced from the pents and hexes with a framed dormer system. I go back and forth of doing this or traps that are angled like the triangles they are replacing and just make dormers for windows.

I like the 4x4 ripping but wonder if the pease method would be easier. I think the Oregon dome method would make interior framing easier.

Bill

[William Fisher]

Paul,

I think you are correct about the 10" blade. Since it is the exact same cut from either side, it would line up perfectly. The cost between 12" tablesaws and 10" is incredible. For making 1 home I can't see spending the money. If I was doing this as a business, I would invest in a heartbeat.

Bill

[Gerry in Quebec]

A few thoughts on the Pease versus Oregon Dome methods of panel construction...

As I see it, the main disadvantage of the Pease system, at least for low-frequency domes including Buckyballs, is that you have a lot of complex sawing to do. First, you have to cut all the strut ends at various compound angles. Second,  if you want the roof sheathing and ceiling panels to sit flush on the triangular frames, you have to bevel-rip both the inner and outer edges of the struts at the right dihedral angle(s). Even the internal bracing of the panels, whether triangles, pentagons or hexagons, requires the cutting of compound angles and ripping down one edge to make the bracing fit snugly within the frame cavity. Cutting a compound angle isn't difficult if you've got the right numbers and a decent compound miter saw. The problem is that it's really easy to make mistakes because you're dealing with both a miter and bevel setting for each cut, left and right, and there are typically many different pairs of such saw settings. So, the Pease method requires a lot of concentration and organization in the shop.

However, for a higher frequency dome, such as a 4v or 5v, you don't have to bevel the narrow edges of your struts if you're using the Pease method. This is because the dihedral angle between triangular panels is so close to being flat (180 degrees). A little bit of construction adhesive on the roof-side strut edges will fill the gap and, combined with nailing, make a strong set of panels. So, it seems to me the Pease method may be practical for higher-frequency domes.

What I like about the Oregon Dome method is that it requires a simple (non-compound) type of cut -- bevel-ripping through the ceiling-to-roof face of a strut -- to get flat panels to approximate a sphere's curvature. Also, the strut-end cuts are all simple bevels, no compound angles. Ditto for the internal bracing. The main disadvantage seems to be the severe limit on the depth of strut you can use to create a good insulation space...unless of course you make a double-frame dome. Another disadvantage is that deep bevel-ripping is probably more dangerous than making the cuts required by the Pease method.
- Gerry in Quebec

On Monday, January 19, 2015 at 9:26:55 AM UTC-5, William Fisher wrote:

[William Fisher]

Gerry,

Great information. Your argument fits well into what I am seeking to do. Since I will have 4-6 studs inside each panel, simple square cuts make it much easier.

[William Fisher]

The more I think about, the more it all makes sense.

Using the ripped 4x4 method is almost required if not using the pease method. Ripping standard 2x4 for the Oregon Dome method masked for very thin beveled edge boards.

What Paul said about using a standard 10" table saw actually sounds safer. You will be making 2 cuts (on each side of the 4x4) but since the board is being cut directly in half, the table block doesn't need to move, you just flip the board over and cut from the reverse side and the cuts meet in the middle. This allows you to set you blade to cut less each time, you just need to cut a little over half way. Since it is cutting less, the saw isn't working as hard therefore less chance of it kicking back on you. Just need a sharp blade.

[norm...@gmail.com]

a third method exists used by John Rich in New Zealand: http://homepages.ihug.co.nz/~jw.rich/details.htm

ken mentions it in this discussion: https://groups.google.com/forum/#!msg/GeodesicHelp/GFdV2WYh-Vc/ajgupDqvVMAJ

There's another easier way to make panels, used by John Rich from New Zealand I believe. Make the panels with 90 degree sides then make filler strips of the proper V shape to fit and fill the spaces between the panels.

Ken,

Just to add more meat to the stew 

[Gerry in Quebec]

Hi Norm,

 

The following was probably part of the same discussion:

https://groups.google.com/forum/#!searchin/geodesichelp/John$20Rich/geodesichelp/nfDHuOVRLmY/M7NDRQZPQ8QJ

The jpg I posted showed panel methods: Pease, Oregon Dome, John W. Rich. File name: Panel-dome-construction-methods.jpg

- Gerry in Quebec

[norm...@gmail.com]

Hi Gerry, that was the thread I was looking for but I think the discussion I linked to was an older one.

[William Fisher]

Doing more of the math for domes using this method, I only have access to standard done calculators online (if anyone knows of one for figuring out these, please share), my point know is actual height, since the top is actually a flat pent and not 5 triangles each beveled upwards, how much height do you loose? Dome size could range from 20-25-30' based on my final decisions.

[Gerry in Quebec]

Bill,

Here's a simple Buckyball calculator, an Excel file. It tells you the height and floor area if you enter either the floor radius or the spherical radius.

- Gerry

On Wednesday, February 18, 2015 at 8:20:39 AM UTC-5, William Fisher wrote:

[William Fisher]

Thanks Gerry. Not a huge difference but enough to be a concern with loft space headroom.

[William Fisher]

Looking for a little more help with angles for this idea.

I would like to build these as a 3/8 dome on a 4' riser wall.

Doing multiple 22' domes that will connect to make one building.

I am struggling to find the wall angles from the top of the riser walls.

Riser walls would have a short wall with the pent on top and a long wall with a trapezoid on top.

Looking back at other threads, I found Gerry had a few drawings using the 5/8 dome. Considering that the trapezoids will act as half hexes in a 3/8 I know the layout changes.

On the mock up I found a wedge was used under the base trapezoid and hex changing the angle from the standard bevel. This is the part that has me scratching my head.

Thanks
Bill

[Gerry in Quebec]

Bill,
The angle between a pentagon panel face and the short riser wall beneath it is 153.4 degrees. Between a trapezoid (half-hex) and the long riser wall the angle is 169.2 degrees. If you're building these Buckyballs as panel domes, the "wedge" angle between the bottom strut of a pent panel and the top strut of its riser wall is 10.1 degrees. Between the trapezoid panel and its riser wall, the wedge angle is 10.8 degrees. The fillet wedge bridges the gap between a panel (based on the Pease method or the Oregon Dome method, for example) and the flat-topped riser wall. Drawing attached.

 

It's possible to build the right slope right into the tops of the riser walls. I once did this for a low-profile 3v icosa dome (triangulated). But it involves cutting a number of compound angles.
- Gerry in Québec

[William Fisher]

Expanding on this, I am looking to put a small cupola on top of one of the Domes, doing the "more than one easy to skin a cat" idea, is it possible to get the tyop of the hexes bevelled to accept the cupola walls directly?

[Paul Kranz]

William:

Like this?

Paul sends...

On Sun, Feb 28, 2016 at 5:42 PM, William Fisher <fisher...@gmail.com> wrote:

Expanding on this, I am looking to put a small cupola on top of one of the Domes, doing the "more than one easy to skin a cat" idea, is it possible to get the tyop of the hexes bevelled to accept the cupola walls directly?

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[William Fisher]

Paul,

Yes, just for some short windows (2' high by 5' wide). Add light and ventilation into a 29.5' dome.

Plan is 2 29.5' Domes, 1 for 2 bedrooms and ath, the other for living room, kitchen and dining area.

Bill

[sergioco...@gmail.com]

Here are some pics of my experiments on this method, very easy (panels are reversible-less diferent panels-, simple 90 degres borders). As strong as other methods certainly -see pics- everybody on it, even jumping- The coating can fill the gaps (elastomeric) making a "structured cover". Dont need wedges, Some drops of PU will make an adjustable angle wedge.

[sergioco...@gmail.com]

More pics

V2 makes lot of gap, higuer frequency, less gap.

[Ken G. Brown]

Looking a lot easier to fabricate than beveled everywhere!

Ken G. Brown

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<2015-03-27 11.35.33.jpg><2015-03-27 11.35.08.jpg><2015-03-27 09.35.33.jpg>

[Radu Sora]

Even easier is to bend steel ribbon. As your strut thickness to dome radius decreases and the frequency increases, the angles and wedges become smaller and can be neglected (by torsion). Another option is to initial bend the steel ribbon on the edge (harder) at the dome radius and then bend triangles (I prefer hexa - penta) perpendicular to the wider side of the ribbon (easier). When assembling them, you get a true ball shape... which is easier to cover with slightly stretchable material because it has no corners. I wanted to register the ideea in Creative Commons, could anyone help me with some information on the procedures?

[Radu Sora]

And by the way, in the second solution, you can weave your dome from 1 long piece of ribbon only, without need to overlap ribbons (2 ribbons to form 1 side). Connectors are just simple circles with 5 or 6 grooves.