Rotegrity / Nexorade Excel table

[Levente Likhanecz]

hiyya everybody,

i attached a good size excel file.

it includes nexorades  from nex7 till nex147 with antiprism results and antiview illustrations as assembly diagrams.

thats the big size - embedded picture.

its a macro enabled workbook, harmless macros just to help jump between pages.

if you disable it still works but you have to navigate sheets by the common tabs.

created in excel 2007. i dont know compatibility with other ms office versions.

pages protected without password just to avoid accidental changes.

happy browsing, levente

p.s. more to come later

[Levente Likhanecz]

here i attached a table with the antiprism geo_m_n created nexorades possible nexN(b,c) outcomes

cheers, lev

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[Adrian Rossiter]

Hi Lev

On Wed, 20 Feb 2019, Levente Likhanecz wrote:
> here i attached a table with the antiprism geo_m_n created nexorades
> possible nexN(b,c) outcomes

The "Proper" column doesn't always respect b>=c, e.g. nex_217_8_9
(although it may not be a feature of the notation, I don't know).

You have the Class I models as NexN(b, 0), but this should be geo_m_0,
which gives NexN(2c, c)

You have the Class II models as NexN(c, c), but this should be geo_m_m,
which gives NexN(4c, c).

Adrian.

--
Adrian Rossiter
adr...@antiprism.com
http://antiprism.com/adrian

[Levente Likhanecz]

thanx Adrian,

i will revise it, i slipped it over.

there was some mistake in the selection method, intention was to select from the 4 possible results (3m..2n..) the best fit value (non negative and b>c).

the Classification was just visual observation, so i will check it once more.

best regards, lev

[Levente Likhanecz]

ok, i was chewing through it, i left formulas of the selection (probably was some "typo" in old formulas)

now everywhere b>=c

i insist my class coloring is valid and equal to your description.

which looks like 

class 1 is spinned from geo_2n_n ..... 2_1.....4_2....6_3....8_4 and the corresponding (b,c) = (n*7,0)

class 2 from geo_m_4m ........ 1_4......2_8.....3_12.....4_16 and (b,c) = (m*7,m*7)

class 3 is all the rest 

cheers, lev

[Adrian Rossiter]

Hi Lev

On Wed, 20 Feb 2019, Levente Likhanecz wrote:
>> On Wed, Feb 20, 2019 at 7:55 PM Adrian Rossiter <adr...@antiprism.com> wrote:
>>> You have the Class I models as NexN(b, 0), but this should be geo_m_0,
>>> which gives NexN(2c, c)
>>>
>>> You have the Class II models as NexN(c, c), but this should be geo_m_m,
>>> which gives NexN(4c, c).

...

> i insist my class coloring is valid and equal to your description.
> which looks like
>
> class 1 is spinned from geo_2n_n ..... 2_1.....4_2....6_3....8_4 and the
> corresponding (b,c) = (n*7,0)
>
> class 2 from geo_m_4m ........ 1_4......2_8.....3_12.....4_16 and (b,c) =
> (m*7,m*7)

If you look again, this is different to what I said. The way I have it
the rotegrity Class is the same as the base model Class.

[Levente Likhanecz]

ok, i will  walk through again your messages. probably i miss something. my understanding based on visual observation. like the the direction of great triangle "parallel" to tessellation field triangles for c1, or right angle for c2, or angled for c3. see attached diagram png.

the sketchup file has the "reverse engineering" attempts from before you explained your notation.

i placed the icosahedron face in to antiprism 1000 radius rotegrity and back-projected from vertices to center of sphere through face. 

there can see how little vertices moves away from base tessellation vertices. (i was hunting hexagons)

so me back to the school, reading over.

best regards, lev

[Levente Likhanecz]

hi Adrian,

do you have some secret switch in antiview where no light / shading applied on struts and balls, just raw colors.

(i have a fancy color picker to display rgb under cursor) 

cheers, lev

On Thu, Feb 21, 2019 at 6:25 AM Adrian Rossiter <adr...@antiprism.com> wrote:

[Adrian Rossiter]

Hi Lev

On Fri, 22 Feb 2019, Levente Likhanecz wrote:
> do you have some secret switch in antiview where no light / shading applied
> on struts and balls, just raw colors.
> (i have a fancy color picker to display rgb under cursor)

No, but if you know of another viewer that will do that maybe it
will import OFF or one of the Antiprism export formats.

[Ashok Mathur]

Dear Lev and Adrian

From yesterday I have been studying the tables given above.

I am trying to choose between a 4v shallow cap (deviced by Gerry) dome and rotogrities.

I am assuming from the table, the vertex to vertex length of a single strut is found by multiplying the unit length by 3.

Also I find that hubs in 4V shallow cap are relatively few. Say between 25 to 30 for the 4V shallow cap. 

But these hubs are difficult to build unless you use a free (to move and adjust) design for the hub. If you build your own such hubs they will cost you a ton and approach over half the cost of bamboos used in struts.

I am considering using Wanger flange designed by Paul Robinson as an alternative. (The WangerFlange: A new way to build. by Paul Robinson — Kickstarter)

But for the rotogrity there are four connectors per full length strut. 

These connectors always join two struts and can be a simple stud pin that has threads at both ends and a smooth surface in between.

Thus there is a real trade-off to be made here.

I am looking at a radius of 600 cms as the upper limit for 4V shallow cap dome using bamboo.

But I can go up to 1000 cms radius with bamboo in Geo 3,0 rotogrity (upper limit for a single strut of bamboo = 5 meters).

If I look at Geo 2,2 rotogrity the upper limit of a single bamboo strut of 5 meters is reached at a radius of 1200 cms.

This is the first time I am making such comparison and choices and I am sure that there are errors in my workings.

Will somebody help by cross checking my workings in a spread sheet that can be shared?

Regards

Ashok

[Adrian Rossiter]

Hi Ashok

On Mon, 30 May 2022, Ashok Mathur wrote:
> I am trying to choose between a 4v shallow cap (deviced by Gerry) dome and
> rotogrities.
> I am assuming from the table, the vertex to vertex length of a single strut

...

> I am looking at a radius of 600 cms as the upper limit for 4V shallow cap
> dome using bamboo.

The Antiprism rotegrity program calculates rotegrities made from
negligibly thin strips, and nexorades made from uniform thickness
rods. Bamboo isn't like either of these things, but if there is
enough wiggle room it might not matter. Also, when making a rotegrity
the model radius will determine how much the bamboo bends. At a
certain radius the bamboo may be fairly straight, or you may like
a slight bend for tension. You could consider making a nexorade and
then reducing/increasing the radius slightly for slight tension.
Barbecue sticks might be useful for experimental models, if you get
the ones that are not too uniform.

[Adrian Rossiter]

On Mon, 30 May 2022, Adrian Rossiter wrote:
> a slight bend for tension. You could consider making a nexorade and
> then reducing/increasing the radius slightly for slight tension.

Radius isn't the best term here, I meant the general model size.

[Adrian Rossiter]

Hi Ashok

On Mon, 30 May 2022, Adrian Rossiter wrote:
> enough wiggle room it might not matter. Also, when making a rotegrity
> the model radius will determine how much the bamboo bends. At a

The bending in a rotegrity is probably also variable depending on
the different (by symmetry) rods, but you might be able to control
this with spacers between rods.

[Ashok Mathur]

Dear Adrian
Thanks for the advice.
Since I have made 30 struts rotegrities of about one meter diameter out of foam board cut into one inch wide and 30 inch strips joined with self the reading screws, I understand the process of fabrication.
I will make a 30 strut rotegrity with 2 inch diameter bamboo poles and study that.
It’s possible that because of inaccurate spacing that the resulting tension will split the bamboo struts.
A bamboo pole will need at minim an extra length of pi into radius of bamboo pole to cross it from outside. Since every strut makes two crossings, it will need that much extra length equally divided into the three sections.
I am at loss to figure out if further adjustments are needed to be made.
If it works, the final radius of the rotegrity is not very important.
Regards
Ashok


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> On 30-May-2022, at 3:46 PM, Adrian Rossiter <adr...@antiprism.com> wrote:
>
> Hi Ashok

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[Ashok Mathur]

Dear Adrian
You have not published any tables for nexorades,
have you?
Are there model commands for me to use to generate such results using both the raddi ?

Regards
Ashok

Sent from my iPhone

> On 30-May-2022, at 6:00 PM, Ashok Mathur <ashokch...@gmail.com> wrote:
>
> Dear Adrian

[Ashok Mathur]

Dear Adrian,
Sorry for for bombarding you with this third message.
I have tried to roughly calculate how much will 5 meter pole bend when used in a 6 meter radius rotegrity.
The circumference of the sphere of radius 6 meters, which equals 360 degrees is 2*pi* radius or roughly 37.70 meters.
1 degrees =37.70/360 = 0.1047 meters
5 meters = 5/0.1047
= 47.7 degrees
So the 5 meter pole will bend by 47.7 degrees
Thanks for patience.

Regards
Ashok

Sent from my iPhone

> On 30-May-2022, at 6:00 PM, Ashok Mathur <ashokch...@gmail.com> wrote:
>

> Dear Adrian

[Adrian Rossiter]

Hi Ashok

On Mon, 30 May 2022, Ashok Mathur wrote:
> You have not published any tables for nexorades,
> have you?
> Are there model commands for me to use to generate such results using
> both the raddi ?

I haven't made any tables. The rotegrity command only generates one
model for a particular nexorade, and scaling the model also implies
scaling the rod radius. If you scale the model up without scaling the
rod rdius there will be gaps between rods, and if you scale it down
without scaling the rod radius then the rods will need to bend.

I am not sure it that answers your question.

[Adrian Rossiter]

Hi Ashok

On Mon, 30 May 2022, Ashok Mathur wrote:
> Sorry for for bombarding you with this third message.
> I have tried to roughly calculate how much will 5 meter pole bend when used in a 6 meter radius rotegrity.
> The circumference of the sphere of radius 6 meters, which equals 360 degrees is 2*pi* radius or roughly 37.70 meters.
> 1 degrees =37.70/360 = 0.1047 meters
> 5 meters = 5/0.1047
> = 47.7 degrees
> So the 5 meter pole will bend by 47.7 degrees

Yes, but where the bamboo is overlapping this will also increase or
decrease the bending, which may be significant (but possibly not in
such a long section).

[Ashok Mathur]

Dear Adrian
The proposed nexor ( the correct term I hope) has a length of 500 cms and a diameter of 5 cms.
The correction to be applied is not large but is finite enough to be figured out and corrected as bamboo may split due to tension.
I was re- reading some things on nexorades and I cam across this idea that as nexors support each other, they can be simply connected with a wire.
I wonder if a large zip tie will also do?
That would be cheap and the hole made in the bamboo can be quite small in size.

Regards
Ashok

Sent from my iPhone

> On 30-May-2022, at 8:26 PM, Adrian Rossiter <adr...@antiprism.com> wrote:
>
> Hi Ashok

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[Adrian Rossiter]

Hi Ashok

On Mon, 30 May 2022, Ashok Mathur wrote:
> The proposed nexor ( the correct term I hope) has a length of 500 cms
> and a diameter of 5 cms. The correction to be applied is not large but
> is finite enough to be figured out and corrected as bamboo may split due
> to tension. I was re- reading some things on nexorades and I cam across
> this idea that as nexors support each other, they can be simply
> connected with a wire. I wonder if a large zip tie will also do? That
> would be cheap and the hole made in the bamboo can be quite small in
> size.

The Antiprism nexorade models refer to straight rods of fixed radius
and minimum length. The model turns out the size it is. For example

rotegrity geo_4 -a n | antiview

The report says

radius: 0.006422830608847 (+/-0.000000000000000)
strut length from: 0.352401145953536

Run the command again, and display using the rod radius and slightly
longer rods and colour by symmetry

rotegrity geo_4 -a n,.4 -O n -c S | antiview -v 0.0064 -e 0.0064

What is the diameter of the base model

rotegrity geo_4 -a n | off_report -S D

vert_max = 1.0211493106641822

So pretty close to radius 1. This means that a 6 m radius model will
have a rod radius of 0.0064 * 6 = 3.8 cm and a rod length of
.4 * 6 = 2.4 m

Using this approach you can expriment with models to find an appropriate
one. Also, the rods are displayed with equal lengths, but some rods can
be made shorter than others.

[Ashok Mathur]

Dear Adrian,
Thanks.
I will study this and get back to you later.
But, on the face of it, the nexor is about 8 feet long and about 3 inches in diameter. It’s going to be divided into 3 parts.
That requires tremendous amount of force to bend such short lengths.

Regards
Ashok

Sent from my iPhone

> On 30-May-2022, at 9:36 PM, Adrian Rossiter <adr...@antiprism.com> wrote:
>
> Hi Ashok

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[Adrian Rossiter]

Hi Ashok

On Mon, 30 May 2022, Ashok Mathur wrote:
> But, on the face of it, the nexor is about 8 feet long and about 3 inches in diameter. It’s going to be divided into 3 parts.
> That requires tremendous amount of force to bend such short lengths.

The bamboo sections will be straight, except that some bending may
be introduced by not having the same thickness of bamboo (rod radius)
at the contact/bind points.

If you want a little bending, to add some tension to the dome, you
could reduce the size of the dome slightly.

[Ashok Mathur]

Dear Adrian
There are a number of constraints induced because I am working with bamboo.
For the construction to last, the bamboo has to be harvested between its age of 3 years and 5 years. In my locality it means that the bamboo diameter will be about 5 cms and the bAmboo will be about 5 meters long. Some poles can be six meters long also.
If the nexor length is restrained at 5 meters certain nexorades of 11 meters radius can be constructed if the diameter of the nexor is ignored.
About 10 cms of extra length has to be distributed among various sections such that all nexors still have the same relative lengths.
In most models that I am looking at at least two nexors differ by very little from each other such they can be replaced by their average. Thus calculations can be reduced.

Regards
Ashok



Sent from my iPhone

> On 30-May-2022, at 10:45 PM, Adrian Rossiter <adr...@antiprism.com> wrote:
>
> Hi Ashok

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[Ashok Mathur]

Dear Adrian

It turns out that the new nexor values and intersections points can be quickly calculated from the rotogrity table using  a simple application of Pythagoras theorem.

A detailed note such that others can check my workings is enclosed.

It also turns out that the corrections are below a milimeter in value.

Its my belief that working with bamboo, good manufacturing practices will not yield accuracies below a milimeter as bamboo shrinks/stretches in the first few years.

Thus rotegrity tables can be used as they are.

Regards

Ashok

[Ashok Mathur]

Dear Adrian,

On reviewing the work done by me, I discovered that I had made an error.

The diagram  shows a right angle triangle where the two known sides are the diameter of the nexor and a Length that is one third of a nexor (i.e. the intersection length).

But the table had used the full nexor length of calculate the new nexor length.

The attached table has been corrected and an additional column inserted in Table 2.

The end results still show that the  innexorade where the nexor is 500cm long and 5 cm in a diameter, the roregrity tables can be used as they are for bamboo where dimensional accuracies are limited.

Sorry for the error that went past me.

Regards

Ashok

Regards

Ashok