Paneling an arch with equilateral triangles

I’m new to Rhino and jumping right into the deep end. I’m trying to model an arch similar to the one pictured below.

The idea is that magnetic tiles like these can be used to decorate the surface similar to the simple sheet metal “bulb” below.

The dimensions of the arch can be modified but ideally the elements of the paneling should match the size and shape of the magnetic tiles reasonably well. Trying to manually create it with all the various shapes and sizes sounds like a nightmare, so my idea is to use paneling tools, lunchbox, kangaroo, or similar to panel the arched surface with only the equilateral triangles and may be some squares/rectangles. I’ve messed around a fair bit with paneling tools with no success. I’m a few days in and making little progress. Once I can get the panels, I’m confident I can export the point array and do the sheet metal conversion in other software I’m more familiar with.

First, is it even possible to make a shape like that with only equilateral triangles? If so, any recommendations?

Maybe you can do something with a net of tetrahedra?

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