How would I find the fundamental region of a tetrahedron for its rotational symmetry group $\mathcal{T}$?
I can think of how to find these regions in 2 dimensions, but I can't wrap my mind around the third dimension.
Thank you very much!
2026-03-31 17:07:53.1774976873
fundamental region for the rotational symmetry group of a tetrahedron
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Can you see how the group of rotations on the equilateral triangle is naturally a proper subgroup of $\mathcal{T}$? Certainly then, the fundamental region of the triangle under this action (seen as a subspace of the tetrahedron) will be a subset of a fundamental region for $\mathcal{T}$. Try to visualise the action of $\mathcal{T}$ on this region. Does it miss any areas of the tetrahedron in its orbit?