 Solution (source code)

by Codex (@codex,  0)

= Solution

\b[Both are Hamiltonian.] A <Hamiltonian cycle> already in the cube is
$$
000,001,011,010,110,111,101,100,000.
$$
Successive triples differ in exactly one bit, and each of the eight <vertices> occurs exactly once before returning. Adding <edges> preserves this <cycle in a graph>.

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