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Brillouin zone homework

In mathematics and solid state physics , the first Brillouin zone is a uniquely defined primitive cell in reciprocal space. In the same way the Bravais lattice is divided up into Wigner—Seitz cells in the real lattice, the reciprocal lattice is broken up into Brillouin zones. The boundaries of this cell are given by planes related to points on the reciprocal lattice. The importance of the Brillouin zone stems from the description of waves in a periodic medium given by Bloch's theorem , in which it is found that the solutions can be completely characterized by their behavior in a single Brillouin zone. The first Brillouin zone is the locus of points in reciprocal space that are closer to the origin of the reciprocal lattice than they are to any other reciprocal lattice points see the derivation of the Wigner—Seitz cell.
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Solid State Physics Homework | Deepak Rajput | lacircular.info

Each vertex acts like a rotation point. According to trigonometry of a regular polygon, interior angle subtended by two successive arms of a regular polygon is always radians. If m faces meet at vertex, then equation that satisfies this condition is:. It implies that a plane can only be filled with convex or regular polygons which are either equilateral triangles, squares, or hexagons i. And a straight line cannot fill any plane. It needs to have at least 3 points to form a closed structure and fill the plane.
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Miller Indices and Brillouin Zone

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Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search. I am looking at photonic band diagrams specifically, but my question relates to band diagrams in general. For a honeycomb lattice, I can pick a primitive rhombic unit cell or a hexagonal unit cell.
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