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BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
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Establish correspondences as follows,
[[math]]
\xymatrix@R=50pt@C=50pt{
S^{N-1}_\mathbb R\ar[r]\ar[d]\ar[dr]&T_N\ar[l]\ar[d]\ar[dl]\\
O_N\ar[u]\ar[ur]\ar[r]&H_N\ar[l]\ar[ul]\ar[u]
}
[[/math]]
by using results from basic geometry and group theory.