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What I would like to do using Geometry nodes is for any platonic solid extrude the selected surfaces, forming arms whose ends are scaled down and then at the end of which are instances of the original platonic solid but also scaled down and correctly aligned to the end of the arm, thus for a tetrahedron I would get this (alas manually created). Manually created

The nodes for this process would be grouped and can then be iteratively used to create objects like these https://www.youtube.com/watch?v=T4A1am45Wtg

For a cube I can can use extrusions as at the end of the arm they can form a cube same as the starting shape, obviously not the same for other platonic shapes.

Here you can see the top 3 are nearely correct but bottom instance position and rotation are incorrect. I have tried many, many nodes (Align Euler to Vector, Vector Math) without success. enter image description here

In addition I also need to identity the face of new instanced mesh that needs to be deleted which is where it joins the arm.

Any help will be much appreciated, John

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If you create a default circle, n-gon filled, $r=1$, extrude up, M,A Merge at Center, and set the resulting vert's $z$ coordinate to sqrt(6)/3 * 1.73205 (multiplying the formula for tetrahedron's of side 1 height, by the side length of the created triangle), you get a tetrahedron:

Not just a tetrahedron, but one aligned with axes so the single align works just right:

If for whatever reason this doesn't work for you, which I'll simulate with some arbitrary rotation, you can align first the peak to the normal, and then the side to the edge:

And this is what happens when you make a fractal out of this:

5 My Little Experiments: Fractal Tree (or broccoli)

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  • $\begingroup$ Thank you Markus for you quick and helpful reply. $\endgroup$
    – fordgud4dall
    Commented Feb 18, 2023 at 20:01
  • $\begingroup$ Sorry I meant to add more! The simpler solution didn't align the instances correctly even using the tetrahedron created as you said. Never mind the more complex solution did align the instances correctly :-) There were some little gaps between the end of the extrusions and the instances but using 'Realize Instances' and a 'Merge by Distance' solved this. Just trying to delete the instances face where it attaches to the extrusion but I should be able to figure it out... $\endgroup$
    – fordgud4dall
    Commented Feb 18, 2023 at 20:09
  • $\begingroup$ @fordgud4dall make sure the base of the tetrahedron lies exactly on Z=0, with the center of this triangle at the origin (this is what happens if you add a circle with 3 vertices in a new project, when 3d cursor is at world origin) $\endgroup$
    – Markus von Broady
    Commented Feb 18, 2023 at 21:13
  • $\begingroup$ Ah! I hadn't spotted that 3D cursor was at 0,0,-0.166666. But when I with the base of the tetrahedron at 0 the gap is bigger at 0.176536 In fact moving all the vertices in edit mode -0.176536 in Z and the gap is 0 - I can't see what Ive done wrong $\endgroup$
    – fordgud4dall
    Commented Feb 20, 2023 at 15:28

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