Compound Angle for the Icosa

[Paul Kranz]

When building a panel for an icosahedron I need a compound angle at the corners, 60° and what, please?

Paul sends...

[Charles Lasater]

21

On Fri, Oct 17, 2025 at 12:39 PM Paul Kranz <pa...@revivetheflame.com> wrote:

When building a panel for an icosahedron I need a compound angle at the corners, 60° and what, please?

Paul sends...

--
--
You received this message because you are subscribed to the "Geodesic Help" Google Group
--
To unsubscribe from this group, send email to GeodesicHelp...@googlegroups.com
--
To post to this group, send email to geodes...@googlegroups.com
--
For more options, visit http://groups.google.com/group/geodesichelp?hl=en

---
You received this message because you are subscribed to the Google Groups "Geodesic Help Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email to geodesichelp...@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/geodesichelp/CAE1FiLVQXBLJ229amtuPNrTpCfMmYW9wAE%2B_U9k4D%3DUEJ-iRSg%40mail.gmail.com.

[Paul Kranz]

Charles: Thanks. Do you have the math for that?

To view this discussion visit https://groups.google.com/d/msgid/geodesichelp/CADgTqM5nTy-oiVsSX4VecKjXU_yCsyJ2uie7vKAY29ohjxYsqA%40mail.gmail.com.

--

Very high regards,

 

Paul C. Kranz, LMFT

Kranz & Associates, LLC

ReviveTheFlame.com

[Charles Lasater]

20.9052

[Charles Lasater]

AutoCAD 

To view this discussion visit https://groups.google.com/d/msgid/geodesichelp/CAE1FiLW_bEUSiE40%3DqoYSQD9TTac8ZXGDErt2ss0GHM-QFYgxg%40mail.gmail.com.

[Michael]

Dihedral angle:

This is the angle between two adjacent faces. For a regular icosahedron, this angle is approximately 183.19

. 

On Fri, Oct 17, 2025 at 3:39 PM Paul Kranz <pa...@revivetheflame.com> wrote:

When building a panel for an icosahedron I need a compound angle at the corners, 60° and what, please?

Paul sends...

[Paul Kranz]

Charles: How is that computed?

To view this discussion visit https://groups.google.com/d/msgid/geodesichelp/CADgTqM7mVbxeoPR%3Doe70xqn52B1OhzMiZ8gO8ay5XccF%2BkGtJQ%40mail.gmail.com.

[Charles Lasater]

I measured the angle between a line from the center perpendicular to the face and a line from the center to the midpoint of the edge.

To view this discussion visit https://groups.google.com/d/msgid/geodesichelp/CA%2BJ%3Dkq8DRvkGhN2vhf1EiMSzxKFUXhfuHc21sHi8%3Du%2BBF90sYQ%40mail.gmail.com.

[Michael]

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

To view this discussion visit https://groups.google.com/d/msgid/geodesichelp/CADgTqM7Zv6G0AArDW0AUoXLHMJXuYdAGF1OQ%2BXz4teouK0Rknw%40mail.gmail.com.

[Charles Lasater]

Divide the dihedral angle (138.19) in half (69.095) and the 90 degree complement (20.905) is the angle Paul is looking for.

To view this discussion visit https://groups.google.com/d/msgid/geodesichelp/CA%2BJ%3Dkq_-H8TU0gsVZxR5uy%3DUQorZ%3D1tFoMCHZ4dezv6MMTp4%3Dw%40mail.gmail.com.

[Paul Kranz]

Thanks, Charles & Michael.

To view this discussion visit https://groups.google.com/d/msgid/geodesichelp/CA%2BJ%3Dkq_-H8TU0gsVZxR5uy%3DUQorZ%3D1tFoMCHZ4dezv6MMTp4%3Dw%40mail.gmail.com.

[Charles Lasater]

Glad to be useful. 

To view this discussion visit https://groups.google.com/d/msgid/geodesichelp/CAE1FiLUD7Y6T6EdQVijiSMw1M3smDh-%2BufkW24UtYSZakYKC2g%40mail.gmail.com.

[Dx G]

Paul,

 I was uncertain if you were looking for a face angle or dihedral angle.  A few suggestions:

1) If you do a search on the group list, you will find a lot of discussion about dome angles and lots of leads.

2) In particular, Gerry posted some real nice spread sheets that will help you check any work you do on your own and usually have the formulas in the cells.  If you have trouble finding these, let me know and I can probably dig out a few.

Here are some leads you might find helpful, but there are many more. Some illustrate the calculations, although usually there is more than one way to do those.

https://gill.readingroo.ms/ENTER/Science/Fuller,%20Buckminster%20Richard%201895-1983/Domes/Geodesic%20Domes.pdf  calculating dome angles
https://www.youtube.com/watch?v=gEH37l6XyVw  paul robinson dome angles

https://www.dirkbertels.net/computing/pentaDome_files/pentaDome_070206.pdf   (see icosahedron details, esp P.22 onward. Gerry's work is simpler for casual use.)

https://woodgears.ca/geodesic/    cutting a wooden Icosa;   https://woodgears.ca/geodesic/60-sided_angles.pdf

-Dx G

[Paul Kranz]

Dx G: Got it, thanks.

Very high regards,

 

Paul C. Kranz, LMFT

Kranz & Associates, LLC

ReviveTheFlame.com

To view this discussion visit https://groups.google.com/d/msgid/geodesichelp/f17e8664-8ac9-4fd6-8440-576f1c5cb705n%40googlegroups.com.