Dome Cookbook of Geodesic Geometry - David Kruschke, 2nd Edition, 1975

[Chris Kitrick]

I was recently able to acquire a complete version of David Kruschke's dome cookbook and performed digital cleanup on the scanned pages. There are no problematic issues with the full text. 

It is available online here. David Kruschke passed away in 2020.

Chris

Dome Cookbook of Geodesic Geometry - David Kruschke, 2nd Edition, 1975

[Chris Belcher]

This beautiful! Thank you so much!

-Chris

Sent from my iPhone

On Jul 1, 2026, at 4:37 AM, Chris Kitrick <ckit...@gmail.com> wrote:



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[Christopher Jones]

Chris

Reading your nice clean copy of the dome cookbook has encouraged me once more to try and understand  Kruschke's methods of subdivision. His goal seems to be to derive by spherical trigonometry the chord factors for v3 and v4 subdivisions. It is also instructive to give more emphasis to the central angles of the corresponding arcs, which he also derives. Here is a link to a 3D model which you can view interactively in the Online 3D Viewer.

https://3dviewer.net/#model=https://chrisjones.id.au/Spherical%20Tessellations/kruschke4_filled_circles.glb

The red great circle arcs are the radially projected edges of the icosahedron. The blue small circles are the 18 flat layers which subdivide the projected spherical triangles.

https://3dviewer.net/#model=https://chrisjones.id.au/Spherical%20Tessellations/kruschke4_filled_circles_with_green_radial_grid.glb

also shows green great circle arcs which are the radial projections of the triangular grid subdividing each triangular face of the icosahedron.

Interestingly, there are 4 triangles and 6 vertices which are shared between the blue and green arcs (not quite in the case of the middle triangle).

Chris Jones
 

[Levente Likhanecz]

the tilt angle of icosahedron plane sets is ATAN(2) = 

63.43494882292201064842780627954668

1 horizontal set and 5 tilted sets 72° apart 

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[Gerry in Quebec]

Hi Chris K. & Chris J.,

 Chris K., thanks for cleaning up the David Kruschke Cookbook and posting the download link. Many years ago I bought an early draft of Dave's publication, full of math edits and other hen-scratchings by Hank Phillips, an engineer who reviewed Dave's manuscript for him. I used it as the basis (inspiration?) for an Excel spreadsheet on the 3v Fuller-Kruschke icosa.

 

Chris J., if that spreadsheet is of any interest to you, you can find it here:

https://groups.google.com/g/geodesichelp/c/zG4Mm__cVHI/m/5WbjH5gTLgIJ

Attachment: 3v-icosa-Fuller-Kruschke-derivation.xls

 

It's a conversation from May 25, 2013: "Fuller-Kruschke method: description, equations & calcs for 3v icosa".

 

Cheers,

- Gerry in Québec

[Christopher Jones]

Kruscke says on PAGE 8 that he wants to create three perfect cutoff planes for the 4 frequency dome, and he achieves this on PAGE 30. His method may seem a bit long-winded, partly because he lists all the intermediate decimal values of calculations. His four lines to get the central angle of arc A3C2, for example, could be replaced by
A3C2 = acos(cos(36) / sin(72)).

With help from ChatGPT, it can be established directly that, as on PAGE 30, Rdash = sqrt((7 + sqrt(5)) / 10) = 0.9610446387915491

Further details at https://chrisjones.id.au/Spherical%20Tessellations/Kruschke.html

On Wednesday, 1 July 2026 at 18:37:24 UTC+10 Chris Kitrick wrote:

[Levente Likhanecz]

the "offset factor" is how far the lesser circle plain from the equator.
and the "radius factor" is at this distance, what is the radius of the lesser circle.

the great circle "frame of the icosahedron" (4V kruschke) is a 20 side poligon.
the lesser circle also.


and there is the icosahedron vertices connecting great circle arc:

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[Levente Likhanecz]

i try to reverse engineer my kruschke 4V dome with chat gpt, to search patterns.

[Levente Likhanecz]

the greenish and reddish great circles (20sided)
the "tent" is 2tip-2tip-2tip. these planes tilted by the 63.435:

the middle vertice makes the lesser circle.
the 2 sides of the magenta rectangle given above.

[Robert Clark]

Here is an optimized version of the 4V 7/12 Kruschke Dome.

It reduces struts lengths from 6 down to 4.

It avoids any scalene panels. All panels are now isosceles.

It achieves this by having some vertices lie outs the unit sphere.

On a 21 foot diameter dome, that equates to just a 1/4 inch.

-Robert

[Gerry in Quebec]

Hi all,

Here's a link to a composite photo of a 50-foot double-framed wooden dome built in 2013-2014 in Vermont using the exact geometry shown here by Robert. The dome is about 50 ft in diameter.

https://groups.google.com/g/geodesichelp/c/jvI0f6HydUw/m/Bl6IzsJ_dwMJ

- Gerry in Québec

[Robert Clark]

Gerry,

It says it differs a little from the Fuller-Kruschke subdivision, but they didn't say how. Is it using just 4 strut lengths and 4 isosceles panels? Maybe there is another article somewhere that goes into more detail?

-Robert

[Gerry in Quebec]

Hi Robert,

The 4v subdivision you described -- 4 chord factors, 4 unique isosceles triangles including CCC equilaterals, radial variation (1.0 versus 1.002045) -- is exactly what was used in the design and construction of that dome in Vermont. I think you and I discussed this design confluence several years back on this forum. Our solutions were identical! 

I'll try to find some more references.

Thanks for all the info on 3D printing of  your connectors. I am learning a lot.

Cheers,

- Gerry in Québec 

[Robert Clark]

Gerry,

I think you're right. We might have discussed it when I first posted it 3 years ago. Sorry I didn't recall that. It's amazing we both came up with the same solution. I utilized SolidWorks' parametric relational constraints in sketches and models to find my solution. I do have a firm grasp of critical polyhedron geometry such as arctan(2). However, I pretty much bypassed any old school trigonometry to find dimensions and angles that worked. I'm curious what CAD software you used to arrive at your own solution?

-Robert