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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.

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Q: How many equilateral triangles in a geodesic dome?
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