My Monthly Modular is a fab use of equilateral triangles that work in clusters of 4 or 5 to make interesting spheroids:
Eight of the modules make a “Jitterbug” – a curious structure that twists into a cube.
Thirty of the modules clustered in fives make a soccer ball (er, sorry, an Icosadodecahedron) which is a lovely thing to behold. (oops, sorry, a icosidodecahedron)
A relatively simple construction, quite quick also and also fairly rigid given how the parts interlock and self-tighten. You can have a go at this yourself here
well, not 2 be picky, but it’s icosidodecahedron 🙂
Also, the “Jitterbug” twists into an octahedron.