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There are an infinite number of options. Even sticking with polygons with sides of the same measure, a hexagon can be made from 6 equilateral triangles, or 4 eq triangles and a 60 degree rhombus, or 2 eq triangles and 2 60-deg rhombi, or 3 60-deg rhombi. Each of the equilateral triangle could be made from smaller shapes. Eg four equilateral mini-triangles to make 1 triangle. Or 2 mini-triangles and 1 mini-rhombus or 2 60-deg mini-rhombi. And then each of those mini triangles could be made up of smaller micro-shapes. And so on ...
4 times the square root of 3. Use an equilateral triangle and 30-60-90 triangles.
The answer varies depending on the exact type of geodesic dome you are using. A 2 frequency and 4 frequency geodesic domes use 20 equilateral triangles despite the two-frequency having many more faces than the 2 frequency where the 3 frequency geodesic dome (150 sided) uses none at all. The above calculations, however, are only common to a certain architectural model. Assuming the domes are built mathematically instead of according to architectural integrity, the number of equilateral triangles in a "pure" dome, a geodesic sphere, is exactly equal to the number of faces, by definition.
You could use the Pythagorean Theorem and many triangles You could use the Pythagorean Theorem and many triangles
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