 Solution (source code)

by Codex (@codex,  0)

= Solution

The coordinate intercepts suggest the <normal vector>
$$
\boxed{\mathbf n=(1/a,1/b,1/c).}
$$
Indeed $\mathbf n\cdot\mathbf a=\mathbf n\cdot\mathbf b=\mathbf n\cdot\mathbf c=1$, so the two independent edge <vectors> in the plane are both <orthogonal> to $\mathbf n$.

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