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For this part, I'll use some different terminology that is a bit more mathematically-oriented:
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<ul>
<li>
<strong>Vertices:</strong> "Dots" where the loop can turn.
</li>
<li>
<strong>Edges:</strong> "Lines" between vertices that may be part of the loop.
</li>
<li>
<strong>Faces:</strong> "Cells" (areas surrounded by edges), with some faces containing numbers indicating the number of edges that must surround them.
</li>
<li>
<strong>Board:</strong> The combination of vertices, edges, and faces, that make up the
<a href="https://en.wikipedia.org/wiki/Planar_graphs">planar graph</a> (grid) of the puzzle.