Miter truss dome


I am trying to figure how to construct a miter joint in grasshopper.:

I have tried to spit the boxes on the dual of the mesh but it didn’t work.

Is this very difficult or am I missing something?
thanks! (18.5 KB)

edit: this is what I have tried: (20.5 KB)

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How accurate does this have to be?


What do you want the result to be like?
Do you need all the bevelled faces to be planar?
For 6 beams coming together it’s generally not going to be possible for all the top and bottom edges to neatly line up, but that’s not necessarily a problem, depending what you want to do with it.

this seems accurate enough, only the angles between the beams are important to me

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thank you - I didn’t know that.
I just want to experiment and try to mill 2 or 3 knots at the university to see if it is possible. It’s a standard 3 axis machine and I can flip it – so they don’t have to be planar.
If the triangle mesh doesn’t work so good I will try the dual mesh, there are fewer beams coming together and it should be easier.

Attached is a model where I split the breps in Rhino.

I deleted the corners manually with the SelSmall command. (32.0 KB)

dome.3dm (10.5 MB)

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You’re opening a can of worms with this!

Planar faces, twisted beams, conical meshes… designing something that you can actually make gets really tricky.

My approach in the past has been to make each triangle in a mesh and work out the angle to cut on each edge so that all the triangles can fit together. Some geodesic domes are made this way…
SnowdonDomes and it works fine for geodesic domes but when you start getting more irregular curvature then the mitres don’t fit properly on the inside (which is why @martinsiegrist has cut the tips off???)

You can get the angles from the mesh…

My intention was to output a list of edge dimensions for each triangle as a sort of cutting list for manufacture…

This doesn’t work on your dual dome made of hexagons and pentagons though.

Good luck. Let us know how you get on!

This uses Sandbox plugin for the mesh topology. (83.8 KB)


Thanks everyone for the support! With the your help and examples made some improvements and got this far: (37.6 KB)

It’s not perfect (cut-surfaces are not planar, uneven connections) but it’ll do for the moment. It might take a while but will try to mill two knots nonetheless.


It would be interesting to work out how non-planar the cut surfaces are. Perhaps you could find the average plane through the corners and cut to that instead of having to machine a non-planar cut? If the error is small, a nice expanding PU glue should fill the gaps :slight_smile:

How were you going to fasten them together? Biscuit joints? (35.2 KB)

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The ends are non planar but not by much … Curve Proximity can be used to determine how much the surfaces are twisted. (41.0 KB)

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