longitudes of rotegrities

[Ramon Masip]

Hello, good afternoon.
I just joined the group and I'm interested in calculating the lengths of the elements of a truncated rotegrity of icosaedron. I'm a retired mathematician, and using elements of spherical geometry, I've calculated, for example, the lengths of the icosahedron  truncated like the one in the figure. Specifically, I've arrived at different results. Therefore, I'd like to know how you calculated them and compare

my resluts are:

pink: 0.1997

green: 0.2284

The ratios between the two lengths are also different, in apro x2%

Thank you very much.

[Levente Likhanecz]

2019 january 30 we had a lengthy explanation from chris kitrick. how to find with excel solver.　

then adrian rossiter made a rotegrity / nexorade modul in antiprism that can solve it lighting fast.　

chris sent such explanations to solve:　

unfortunately i cannot link here that conversation (thread)

maybe somebody will find how to.　

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[Levente Likhanecz]

https://antiprism.com/programs/rotegrity.html

[Chris Kitrick]

Hi Ramon,

A more thorough description of how nexorades (aka rotegrities) are computed can be found in the following conference paper:

• Non-Linear Solution to Spherical Coverings and Application to Forms

Cheers,

Chris

[Chris Kitrick]

Hi Ramon,

There is an extended version of the conference paper I mentioned is covered in Chapter 10 of the 2nd edition of Edward Popko's book Divided Spheres.

Cheers,

Chris

[Levente Likhanecz]

donno, i have an old excel file with macroes (to navigate between sheets)　

there are some calculated rotegrities (for reference)

https://docs.google.com/spreadsheets/d/1WTXfiio-VzCcvlwbnXgjmRWjHfR6x7gf/edit?usp=sharing&ouid=110688085901323339922&rtpof=true&sd=true

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[Robert Clark]

There's also this modified version (on the right) that uses one strut instead of two.  Despite the rectangular openings, the geometry is as stable as other nexorades.

[Levente Likhanecz]

0.252321690765958

0.283344374568195

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[Levente Likhanecz]

above are chord lengths. 

these are arc lengths:

0.252995879706

0.284300873626

[Ramon Masip]

I agre, the longitudes are as You say, I had an error of càlculs, thanks for all your help 

0.252321690765958

0.283344374568195

Ramon S Masip

El dv, 30 maig 2025 a les 19:17 Levente Likhanecz <likh...@gmail.com> va escriure:

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