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Draw a two-dimesnsional haxagonal lattic...

Draw a two-dimesnsional haxagonal lattice. Try to visualize the possibility of pentagonal two-dimensional lattice.

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To solve the question of drawing a two-dimensional hexagonal lattice and visualizing the possibility of a pentagonal two-dimensional lattice, we can break it down into clear steps: ### Step 1: Drawing a Two-Dimensional Hexagonal Lattice 1. **Start with the Basic Shape**: Begin by drawing a hexagon. A hexagon has six sides and can be represented as a regular polygon. 2. **Replicate the Hexagon**: To create a lattice, replicate this hexagon in a systematic way. Place additional hexagons adjacent to the first one, ensuring that they share sides. 3. **Visualize the Lattice Points**: Identify the lattice points. In a hexagonal lattice, each vertex of the hexagon represents a lattice point. Additionally, the center of the hexagon is also a lattice point. 4. **Count the Lattice Points**: Each hexagon contributes 1 lattice point at its center and shares its vertices with adjacent hexagons. Thus, for every three hexagons sharing a vertex, the contribution is 1/3 per hexagon for each vertex. ...
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