Compound angle, 3 dimensional triangle

Hi Guys, Im trying to draw these in Sketchup. Im a new user and the angles are proving to be difficult as they do not sit on the red, blue green axis. Assuming the overall cube dimension of the light is 300mm. How would I go about working out the compound angles?

I would model the pieces letting them run past the corners. Then use one as a guide for trimming the neighbor. These appear to be regular tetrahedra so you can work with equilateral triangles to start.

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If these are tetrahedrons, see this SU file for ideas.

TĂ©trahedron.skp (88.7 KB)

3D model (SU8): triangles.skp (50.3 KB)

How to…
using Polygon, Arc Pie tools and Curic Mirror plugin, and Copy (Ctrl+V), Paste in Place.
tri-05b

tri-05c

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You are a legend, thanks so much. Spent a day on this and got nowhere.

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See another SU file for ideas.

Tetrahedral frame.skp (103.7 KB)

Another one. Click in sequence on the scenes tabs of this SU file for ideas.

Tetrahedral frame 2.skp (107.6 KB)

I learned a simple way to make a tetrahedron from Ann Tyng* by inscribing it in a cube.
See this post I did back in 2017:

A cube has six equal faces and a tetrahedron 6 equal edges, one for each face of a cube.

*Ann Tyng, was a classmate of my mother’s at Harvard Graduate School of Design, where they were among the first year of women to attend. Later she was a teacher of mine at U Penn. When you see things in Lou Kahn’s work like the tetrahedral ceiling of the Yale Art Gallery, I believe you’re seeing the influence of her on his work.