The height of a geodesic dome.

[John Hurt]

When calculating the height of a 2v, 4v, or 6v geodesic dome, I am multiplying the radius by "1" to get the dome height.  Here are the multipliers I am using for the height of the other types of domes:

3v 3/8       .828

3v 5/8       1.172

3v 4/9 Kruschke      .81241

3v 5/9 Kruschke      1.187592

4v 5/12 Kruschke      .72361

4v 7/12 Kruschke      1.27639

5v 7/15       .89565

5v 8/15       1.11126

Are these values correct?

Thanks,

John

[Gerry in Quebec]

Hi John,
Your height numbers look good. I'm posting three drawings to give a bit of precision for  3v method 1, the 5v method 1 and 5v Kruschke-style dome.
Cheers,
- Gerry

[John Hurt]

Gerry,

Thanks for the drawings and information about the Kruschke 5v dome.  

The 5v with a flat base at 4 different truncations is an amazing design, and has a lot of possibilities. 

Thanks again,

John Hurt

[Levente Likhanecz]

hi Gerry,
the 5V Kruschke (4 level flat), did you feed your own off file to
display in antiprism, or Adrian has already built in model?

cheers, lev

[Gerry in Quebec]

Hi Lev,

I put together the model of the 5v truncatable dome (Kruschke-style) using spherical trigonometry and Excel's Solver feature. I then imported the resulting off file into Antiprism to complete and display the model. 

Many years ago Taff assembled a collage of Kruschke-style domes in SketchUp including the 5v. He reposted the SketchUp file here:

 https://groups.google.com/g/geodesichelp/c/UmbvayfzGGU/m/EYz-kCNxHwAJ

The geometry of the 5v Kruschke-style truncatable was used by Fuller & Sadao for the Religious Center at the Edwardsville campus of the University of Southern Illinois, USA.

Cheers,

- Gerry

[Levente Likhanecz]

thanx Gerry,
i recall the thing, we've discussed there earlier, i built my own
solver sheet then with arbitrary precision to any digits. (i've
iterated the central equilateral triangle)
may be Chris told us no solution for higher than 5V frequencies, cause
Taff has a 6V there which is either a bit cheating away from sphere
surface or vertices not truly at intersection.

because this 5V is the best looking kind of Kruschke, i tought may be
Adrian has put a model of it in antiprism built in geo models.
but you stuffed that there.

cheers, lev