Planar cubic graphs given by faces

Task number: 4249

Is there a cubic (i.e. \( 3 \)-regular) planar graph that contains:

  • Variant

    Just 12 hexagonal faces (and no other)?

  • Variant

    Just 12 pentagonal faces (and no other)?

  • Variant

    One pentagonal face and ten pentagonal faces (and no other)?

Difficulty level: Moderate task
Solution require uncommon idea
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